# Right Triangles Teacher Resources

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EngageNY

#### EngageNY Geometry Module 2: Similarity, Proof, and Trigonometry

The Geometry Module 2: Similarity, Proof, and Trigonometry collection includes 36 lessons that are divided into five topics: Scale Drawings, Dilations, Similarity and Dilations, Applying Similarity to Right Triangles, and Trigonometry....

Lesson Planet

#### Getting into Trig

Starting with right triangles (SOH-CAH-TOA) and working up to the concept of radians, this collection introduces students to trigonometric ratios and supports them in learning to evaluate trigonometric functions.

EngageNY

#### EngageNY Geometry Module 4: Connecting Algebra and Geometry Through Coordinates

Teach young mathematicians how to use coordinate geometry to program a robot that is bound in the room in which it sits . Help comes in the form of the 15 lessons in the Module 4: Connecting Algebra and Geometry through Coordinates...

EngageNY

#### EngageNY Precalculus and Advanced Topics Module 4: Trigonometry

Introduce advanced math students to the power of trigonometry! The 14 lessons in the Module 4 collection are divided into three topics: Trigonometric Functions, Trigonometry and Triangles, and Inverse Trigonometric Functions. Each lesson...

Lesson Planet

#### Common Core Math: 8th Grade

Check out the Common Core with a collection that represents all the 8th grade math standards. Most resources engage multiple standards but the main one is listed on the notes section of each tab.

Lesson Planet

#### Pythagorean Theorem: Not All Sides are Equal

You'll find fundamentals and advanced activities focused on the Pythagorean Theorem in this collection, which was designed for high schoolers but helpful for young geometrists of all ages!

Lesson Planet

#### Common Core Math: 6th Grade

Need some help aligning your 6th grade math curriculum to Common Core? Here is a collection complete with a resource for every standard in the curriculum. While many of these resources cover multiple math standards, the main one...

Lesson Planet

#### "Grade 9-12, Claim 2 & 4: Problem Solving & Communication Reasoning Supports"

Small but mighty, a collection of three resources features presentation slides that prepare high schoolers for the Smarter Balanced assessment. Claim 2 features problem solving questions drawn from all content areas. Claim 3 focuses on...

Lesson Planet

#### Grade 8, Claim 1: Concepts and Procedures Item Slide Shows

Ten resources make up a collection of student and teacher-friendly slides that prepare eighth graders for the Smarter Balance assessment. Learners review rational and irrational numbers, convert repeating decimals to fractions, as well...

Lesson Planet

#### Find the Area of a Right Triangle

Help your class develop a greater understanding of the area of a right triangle. The video starts by reviewing the area of a rectangle and noting that the rectangle is made up of two congruent triangles. Learners are then shown that in...

Lesson Planet

#### How Do You Determine if a Triangle Is a Right Triangle if You Know its Sides?

Use the Pythagorean Theorem formula to check if this given triangle, with the given lengths of each side, is a right triangle. It's as simple as plugging the given values into the formula and doing the math to see if the solution checks...

Lesson Planet

#### Special Right Triangle 45-45-90: Lesson

Square roots connect squares and right triangles. Using the Pythagorean Theorem, the video shows the relationship between the sides and hypotenuse of a 45-45 right triangle. The portion of a larger geometry playlist applies the...

Lesson Planet

#### Pythagorean Theorem for Solving Right Triangles: Solving the Triangle

Observe the change in the trigonometric ratios as angles vary. An interactive provides the values of trigonometric ratios for both acute angles in a right triangle. Pupils create a right triangle to match given criteria and find the...

Lesson Planet

#### Special Right Triangles and Right Triangle Trigonometry

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

Lesson Planet

#### Perimeter and Area of a Right Triangle

Make sure the coordinates are right when calculating distances. Given a right triangle on the coordinate plane, pupils determine the perimeter and the area. The scholars calculate the length of each side using the coordinates of the...

Lesson Planet

#### Lengths of Sides in Isosceles Right Triangles: Paper Football

Fuse sports and geometry by having your class create paper footballs—that are actually isosceles right triangles! Scholars use an interactive to create an isosceles right triangle to model a paper football. From the information in the...

Lesson Planet

#### Relationships of Sides in 30-60-90 Right Triangles: Truck on a Mountain Road

Determine the change in elevation on a mountain road. Individuals use the interactive to simulate a truck driving up a mountain road with a 30-degree incline. They determine missing sides of a 30-60 right triangle to find horizontal and...

Lesson Planet

#### Right Triangle Applications: Lessons 1 and 2

Use right triangles for more than just mathematical problems. The first two lessons of a unit ask pupils determine distances between cities by using the Pythagorean Theorem and a map. To cement understanding, learners use trigonometric...

Lesson Planet

#### Special Right Triangles

Using the Pythagorean Theorem to solve for missing angles, high schoolers evaluate right triangles and their properties.

Lesson Planet

#### Ratios of Right Triangles

High schoolers find the angle measures of a right triangle given two side lengths. In this finding the angle measures of a right triangle given two side lengths lesson, students record the ratio of a leg and hypotenuse of a right...

Lesson Planet

#### Investigating Segments in a Right Triangle

High schoolers explore the concept of right triangles as they construct a right triangle using Cabri Jr. Learners find the midpoint of the hypotenuse and construct a line from the midpoint to the vertex of the right angle. They then...

Lesson Planet

#### Ratios in Right Triangles

Learners calculate the sides of right triangles in this trigonometric ratios lesson. They use Cabri Jr. software and TI-83 or TI-84 calculators to find the side lengths and their ratios to each other for various triangles. The provided...

Lesson Planet

#### Sin, Cos, and Tan of Right Triangles

High schoolers explore the sine, cosine, and tangent relationships of a right triangle. In this sine, cosine, and tangent relationships of a right triangle lesson, students construct a right triangle. High schoolers develop the sine,...

Lesson Planet

#### 30-60-90 Right Triangles in Cabri Jr.

Young mathematicians draw and label right triangles using Cabri Jr. technology. They create other special right triangles and identify the length of the hypotenuse and each leg. Students explore the ratios to determine how the hypotenuse...

Lesson Planet

#### Basic Right Triangles

Elementary schoolers examine the attributes of triangles. In this triangle lesson, learners compare regular triangles and right triangles. They explore vertices and angles and investigate obtuse and acute angles. Pupils draw multiple...

EngageNY

#### Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles

Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...

EngageNY

#### The Area of Right Triangles

Slice and dice area. Pupils cut rectangles in half and determine the area of the resulting right triangles. They use what they discovered to develop a formula to find the area of a right triangle in the second lesson in a 22-part series.

Lesson Planet

#### Interior Designers: Working with Right Triangles

Adding a career application, the resource explores the idea of making squares from the sides of a right triangle to show that the sums are equal. The question refers to designing a mural that leads the class into their own drawing of a...

Lesson Planet

#### Inscribing and Circumscribing Right Triangles

High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve their...

Lesson Planet

#### Special Right Triangle 30-60-90: Lesson

It is special—given one length, you can find the other two. A segment of a basic geometry playlist provides the ratio of the lengths of sides of a 30-60 right triangle. The presentation shows how to use the ratio to find side lengths...

Lesson Planet

#### Special Triangle Ratios: Special Right Triangle Ratios

Go from one side length to any other side length with special right triangles. Individuals use the interactive to investigate the ratio of sides in 45-45 and 30-60 right triangles. Scholars make generalizations about the types of special...

Lesson Planet

#### Dilations Using Right Triangles

Don't argue with a triangle that has a 90-degree angle. It's always right. Scholars first use right triangles to help draw dilations of points. They continue the lesson by applying this skill to draw dilations of polygons.

Lesson Planet

#### Right Triangles, Bearings, and Other Applications: Sailing Race

Help your class get their bearings when it comes to right triangles. Pupils determine distances traveled or components given the bearing of a sailboat using an interactive. The scholars develop a sense of finding the bearings of a given...

Lesson Planet

#### Distance Formula: Right Triangles

Go the distance with a far out resource. Individuals use an interactive to create right triangles on a coordinate plane to help find distance between two points. Challenge questions aid them in developing the distance formula.

Lesson Planet

#### Isosceles Right Triangle

In this isosceles right triangle worksheet, 10th graders solve and complete 5 different constructions of composition and decomposition. First, they make 4 congruent isosceles triangles with the model on the left. Then, students create...

EngageNY

#### Prove the Pythagorean Theorem Using Similarity

Amaze your classes with the ability to find side lengths of triangles immediately — they'll all want to know your trick! Learners use the Pythagorean Theorem and special right triangle relationships to find missing side lengths.

Lesson Planet

#### What are the Legs and Hypotenuse of a Right Triangle?

What are all the parts of a right triangle called? What makes it a right triangle? Legs? Triangles have legs? Hypotenuse? Pythagorean Theorem? The instructor diagrams and identifies all the parts of a right triangle for you.

Lesson Planet

#### How Do You Find the Sine of an Angle in a Right Triangle?

A trigonometric ratio is a ratio between two sides of a right triangle. In this problem, find sin(A) in the given right triangle. Use the ratio of the opposite side over the hypotenuse.

Lesson Planet

#### How Do You Find a Missing Side of a Right Triangle Using Cosine?

Trigonometry? What's trigonometry. Well, something to do with triangles, right? Right! Right triangles! In this problem, find the missing length of one of the sides. So set this up as a ratio: cosine(A) = adjacent side length divided by...

Lesson Planet

#### SAT Prep: Test 1 Section 9 Part 3

If it takes a long time to complete the problems on the math SAT, it doesn't matter if they are correct - the problems that are left over will count against the student's score. Sal takes care to show quicker ways to complete problems...

Lesson Planet

#### Right Triangle Geometry

Young scholars study the basic principles of right triangle geometry needed to solve for unknown values of a right triangle. They apply and master the principles of right triangle geometry by solving problems.

Lesson Planet

#### Pythagorean Theorem and Special Right Triangles

Learners review the Pythagorean Theorem and apply it to word problems involving special right triangles.

Lesson Planet

#### Special Right Triangles

Students identify the different parts of a right triangle. In this geometry lesson, students use the Pythagorean Theorem to identify missing sides and angles of a right triangle. They work with irrational and rational roots.

Lesson Planet

#### Trigonometry Ratios in Right Triangles

In this trigonometry ratios in right triangles worksheet, 10th graders solve 10 different trigonometric ratios that apply to right triangles. First, they define a trigonometric ratio and its three most common ratios, sine, cosine, and...

Lesson Planet

#### Right Triangles

In this right triangles worksheet, 10th graders solve 10 different problems that include determining the means proportionally in each right triangle. First, they use the given information to determine the measure of each line segment....

Lesson Planet

#### Trigonometry Ratios in Right Triangles

In this trigonometry ratios in right triangles worksheet, 10th graders solve 6 different right triangle problems. First, they find the values of x and y in each triangle, rounding each to the nearest tenth. Then, students locate the...

Lesson Planet

#### Right Triangle Sports

Who knew math could help with sports? An invigorating set of lessons encourages learners to apply right triangles in baseball, volleyball, hockey, football, and soccer. They use the Pythagorean Theorem, Pythagorean triples, special right...

Lesson Planet

#### Trigonometry and Right Triangles

In this trigonometry and right triangles worksheet, students solve and complete 12 different problems that include various right triangles. First, they write the sine or cosine equation for each right triangle illustrated. Then, students...

Lesson Planet

#### Right Triangle Stuff

In this right triangle worksheet, learners use trigonometric ratios to find the hypotenuse, right angle, opposite leg and angles. This one-page worksheet contains eight problems. Answers are provided at the bottom of the page.

Lesson Planet

#### Right Triangles

In this right triangle worksheet, students use trigonometric ratios to determine the length of a missing side or a triangle or determine angle measurement. They match the vector with the correct component form of the vector. Students...

Lesson Planet

#### Special Right Triangles

In this special right triangles learning exercise, 10th graders solve 10 different problems that include solving equations that are special right triangles. First, they determine the exact value of each problem. Then, students use the...

Lesson Planet

#### Right Triangles

In this right triangles worksheet, 10th graders solve and complete 39 different problems. First, they find the missing variables and trigonometric ratios. Then, students select the correct ratio from the four ratios provided for each...

Lesson Planet

#### Principles of Square Roots Lesson Plan

Middle and high schoolers investigate all the different places in math that square root is present. For this geometry lesson, pupils discuss square roots as it relates to a right triangle and construction. They go over altitude, rise,...

Lesson Planet

#### The Pythagorean Theorem

What special relationship exists among the sides of a right triangle? Explore this relationship using a computer applet, cut-and-paste activity, and video tutorial to develop the Pythagorean Theorem and its significance to right triangles.

Lesson Planet

#### Learning Unit: The Pythagorean Theorem

Middle and high schoolers research the life of Pythagoras and the Pythagorean theorem. They write a short biography of Pythagoras and learn to apply the theorem in their study of right triangles.

Lesson Planet

#### Inverse Trig Functions

Learners solve and graph 10 different problems that are the inverses of various trig functions. First, they determine which equation is equivalent to a given equation. Then, they find an angle of a right triangle, given its leg lengths....

Lesson Planet

#### 7-2 Self Check Pythagorean Theorem Multiple Choice

Middle and high schoolers use the Pythagorean Theorem to determine the length of the sides of a right triangle. They solve distance problems. This one-page instructional activity contains 10 multiple-choice problems. This is...

Lesson Planet

#### Special Right Triangles

In this special right triangles worksheet, 10th graders solve 7 various problems with various types of right triangles. First, they identify the two special types of right triangles, the 45-45-90 degree triangle and the 30-60-90 right...

Lesson Planet

#### Similar Right Triangles-Introductions to Trigonometry

For this geometry worksheet, students examine similar right triangles as the basis for the foundation of trigonometry. Students define the basic trigonometric functions and use a calculator to find the trigonometric value of an angle....

Lesson Planet

#### Practice 7-4: Similarity in Right Triangles

In this right triangle learning exercise, students determine the similarity of given worksheets. They find the length of one side of a triangle. This one-page learning exercise contains 19 multi-step problems.

Lesson Planet

#### Been Caught Stealing

You're safe, when calculating the odds of stealing second base! Learners compare the rate of a runner to the distance the ball travels, in a instructional activity that explores right triangles and measurement. Full of discussion...

Lesson Planet

#### Adjacent Right Triangle Problems

The instructor identifies the terms used to solve for the angle of adjacent right triangles. He does not have an example to solve a problem.

Lesson Planet

#### Triangles

Why are there so many different types of triangles? Be that as it may, beginning geometers need to understand the differences between equilateral, isosceles, scalene, and right triangles, and they get a visual approach with this...

Lesson Planet

#### Triangle Designs - Enrichment 16.5

Upper graders cut out cards with the scalene, isosceles, equilateral, acute, obtuse, and right triangle terms, choose a card, and complete the chart with the number of sides or angle and draw the design. They complete one chart.

Lesson Planet

#### Similar Right Triangles and Trig Ratios

Is it possible to be the same yet different? Absolutely! The activity asks learners to explore the relationships between side ratios of triangles they have drawn. Because individuals all draw a triangle with the same angle measures, they...

Lesson Planet

#### Reteaching 5.4 The Pythagorean Theorem

In this Pythagorean Theorem worksheet, pupils use the Pythagorean Theorem to determine the length of a missing side of a right triangle. This three-page worksheet contains examples, explanations, and 25 problems. Answers are provided on...

Lesson Planet

#### How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?

Given an isosceles triangle, and the value of one angle, find the missing values. There are some special properties about isosceles triangles. Use the triangle sum theorem to solve this problem. Watch this video to see how the instructor...

Lesson Planet

#### How Do You Find the Tangent of an Angle in a Right Triangle?

What's a trigonometric ratio? It is a ratio between two sides of a right triangle. In this problem, find tangent(A) in the given right triangle. Use the ratio of the opposite side divided by the adjacent side to find tan(A). The...

Lesson Planet

#### How Do You Find a Missing Angle in a Right Triangle?

The triangle sum theorem states that the interior angles of a triangle add up to 180 degrees. So it seems logical that if there are two known values given for the interior angles of a triangle, the third value could be found using this...

Lesson Planet

#### How Do You Find the Cosine of an Angle in a Right Triangle?

What's a trigonometric ratio? It is a ratio between two sides of a right triangle. In this problem, find cosine(A) in the given right triangle. Use the ratio of the adjacent side divided by the hypotenuse to find cos(A). The instructor...

Lesson Planet

#### How Do You Find a Missing Side of a Right Triangle Using Tangent?

Identify the variables, identify the given values and use a formula to find the missing length in this right triangle problem. What formula? The tangent ratio, which is normally used to show a ratio between two sides of a right triangle,...

Lesson Planet

#### How Do You Find the Length of a Leg of a Right Triangle?

A right triangle. Two given measurements for two side lengths and one unknown length. Use the Pythagorean theorem to solve this problem and find the missing value. Squares and square roots are used in this problem and don't worry when...

Lesson Planet

#### Right Triangles are Cool Because of Pythag's Rule

Tenth graders investigate The Pythagorean Theorem. In this geometry lesson, 10th graders explore the lengths of the sides of right triangles. In this two part lesson, the students discover the Pythagorean Theorem and also determine if...

Lesson Planet

#### Right Triangles Trigonometry

The class uses the computers to access GeoGebra Dynamic Worksheets to learn the basics about vectors. They will look at graphs and make computations to problem solve to find coordinates of vectors.

Lesson Planet

#### Intro to the Trigonometric Ratios

This video introduces the basics of trigonometry. It starts by defining a right triangle and showing two different examples of finding the ratios of sine, cosine, and tangent using the SOH-CAH-TOA mnemonic. This resource could be used as...

Lesson Planet

#### 45-45-90 Triangles

The process for calculating values using a right triangle with angles of 45 degrees is covered in this third portion of the Pythagorean Theorem series. Here, Sal uses algebra to calculate the value of an angle. The solution to the sample...

Lesson Planet

#### Applying the Pythagorean Theorem in a Mathematical Context

Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...

Lesson Planet

#### Pythagorean Theorem

In this measurement instructional activity, learners examine the Pythagorean Theorem, perimeter, and areas of right triangles. They record their measurements and research their findings on a grid.

Lesson Planet

#### Roots and the Pythagorean Theorem

In this roots and the Pythagorean Theorem activity, learners solve 15 different types of problems related to square roots and applying the Pythagorean Theorem. They first determine the square root of each number and then, the cube root....

Lesson Planet

#### Finding Angles in Right Triangles

In this geometry worksheet, 10th graders use right triangle trigonometry to solve application problems in which they find the measure of the missing angle in a right triangle. The two page worksheet contains five free response...

EngageNY

#### The Area of Acute Triangles Using Height and Base

Use the height of an acute triangle to create two right triangles. The third lesson in a series of 22 has pupils divide acute triangles into two right triangles. Scholars calculate the areas of the two right triangles and add them...

EngageNY

#### The Converse of the Pythagorean Theorem

Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a instructional activity that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether...

Lesson Planet

#### E=mc² is Incomplete

The most famous equation in the world isn't telling us the whole story! What if an object is actually moving? The narrator introduces momentum into the mix, resulting in the sad truth that traveling at the speed of light is almost, but...

Lesson Planet

#### The Right Triangle

Solve for the opposite and adjacent sides and angles of a right triangle. With three right triangles and six opportunities to solve the problems, a straightforward instructional activity prompts young mathematicians to practice the...

Lesson Planet

#### Right Triangles & Pythagorean Theorem

In this math activity, middle schoolers find the missing angles for the right triangles using the Pythagorean Theorem. Then they label the adjacent and opposite angles.

Lesson Planet

#### Find the Missing Side of the Right Triangle

In this find the missing side of the right triangle worksheet, students use the Pythagorean theorem to find the missing side, given the other 2 lengths, for 4 triangles.

Lesson Planet

#### Squares, Rectangles, and Right Triangles

Youngsters identify and draw polygons including squares, rectangles, and right triangles. In this polygons lesson plan, everyone draws these shapes that have right angles in their math journals.

Lesson Planet

#### What are Acute, Obtuse, and Right Triangles?

Triangles are classified by their angle measurement as well as by the length of their sides. Here are some names that identify the types of triangles: right, isosceles, equilateral, scalene, obtuse, and acute. Watch this video to learn...

Lesson Planet

#### How Do You Find a Missing Side of a Right Triangle Using Sine?

What's a trigonometric ratio? It is a ratio between two sides of a right triangle. In this problem, find sin(A) in the given right triangle. Use the ratio of the opposite side divided by the hypotenuse to find sin(A). The instructor...

Lesson Planet

#### You Can't Go Wrong with a Right Triangle 1

Fourth and fifth graders study the Pythagorean Theorem and apply it to find the missing side of a right triangle.

Lesson Planet

#### Special Right Triangles

In this special right triangle worksheet, students use the trigonometric functions to determine angle measurement or the length of one side of a right triangle. This one-page worksheet contains 18 problems. Answers are provided at the...

Lesson Planet

#### Intro to 30-60-90 Triangles

As the fourth part of a series on the Pythagorean Theorem, Sal continues an exploration of the ways to calculate the length of sides of a right triangle using algebra. He also explores using this theorem to solve problems involving a...

Lesson Planet

#### Intro to 30-60-90 Triangles

Lesson Planet

#### 45-45-90 Triangles

Lesson Planet

#### Mixed Right Triangles

In this geometry activity, 10th graders use right triangle trigonometry to find the missing angle measure or side length in right triangles. The one page interactive activity contains ten questions. Answers and hints are included.

Lesson Planet

#### Geometry Chapter 7 Practice Test

For this geometry worksheet, 10th graders review problems that review a variety to topics relating to right triangles, including, but not limited to the Pythagorean Theorem, simplifying radicals, special right triangles, and right...

Lesson Planet

#### HL Triangle Congruence: Lesson

Use the right congruence statement. The video introduces the Hypotenuse-Leg Theorem to prove two right triangles are congruent. Part of a geometry playlist shows that it does not matter which leg to use when proving congruence.

Lesson Planet

#### Lengths of Triangle Sides Using the Pythagorean Theorem: Find the Missing Side

What is the relationship between the sides of a right triangle? Learners use an interactive to create models of right triangles and view the relationship between the lengths of the sides. They finish by using the Pythagorean Theorem to...

Lesson Planet

#### Identifying Sets of Pythagorean Triples: Matching Problem

What sets of whole numbers make up the measures of side lengths in right triangles? Pupils use an interactive triangle to learn about Pythagorean triples. Individuals find missing values in triples and learn more about Pythagorean...

Lesson Planet

#### Justifying HL Congruence

What is so special about right triangle congruence? Pupils use what they know about transformations and right triangles to develop a proof of hypotenuse-leg congruence. The proof provides the given of two angles that measure 90 degrees...

Lesson Planet

#### Inverse Trigonometric Ratios: Lesson

Finding the inverse of trigonometric ratios is not the same as finding the reciprocal. The presentation introduces how to find the angle of a right triangle given sides. Part of a larger playlist on geometry, the video uses the inverse...

Lesson Planet

#### Pythagoras' Theorem

Use a right method to find a distance. Given a right triangle, class members find the length of one side given the measurement of the other two sides—the missing side may or may not be the hypotenuse. A video reminds the pupils how to...

Lesson Planet

#### Area of Right Triangles

For this are of right triangles worksheet, students read graphs and explore congruent triangles. They find the area of rectangles and of right triangles. This one-page worksheet contains explanations, instructions, and 8 problems.

Lesson Planet

#### Right Triangles

In this right triangles worksheet, 10th graders solve and complete 14 various types of problems. First, they find the perimeter of the isosceles trapezoid shown. Then, students find the measures of each marked side of a right triangle....

Lesson Planet

#### Area of Right-Angled Triangles

There's a trick to solving the area of a triangle, and it involves a skill your geometers have already mastered. Help them discover the connection between finding a rectangle's area and finding a right triangle's area as they solve for...

Lesson Planet

#### Pythagorean Theorem

In this Pythagorean theorem worksheet, students solve and complete 20 different problems that include using the Pythagorean theorem to solve them. First, they use the Pythagorean theorem to determine the value of x in each right...

Lesson Planet

#### Geometry Review Exam

In this geometry review worksheet, 10th graders solve and complete 100 various types of problems studied in geometry. First, they find the slope-intercept form of a line passing through two points and parallel to a given line. They also...

Lesson Planet

#### Right Angle Triangles an the Cosine Ratio

In this right triangle worksheet, learners use trigonometric ratios to find the missing measurement of right triangles. This nine-page worksheet contains 10 multi-step problems. Answers are provided at the end of the worksheet.

Lesson Planet

#### What's the Trig?

Learners determine the trigonometric relationships within a triangle as they construct a right triangle on the Ti-89. They find the sine, cosine, and tangent of various angles of their triangle construction.

Lesson Planet

#### Simplifying Expressions

In this simplifying expressions worksheet, students solve and complete 10 various types of problems. First, they simplify each expression and solve. Then, students write each number in scientific notation. In addition, they find the...

Lesson Planet

#### Trigonometry

For this right triangles worksheet, students use trigonometric ratios to determine the length of a side of a triangle or a missing angle measurement. This two-page worksheet contains 20 problems.

Lesson Planet

#### Trigonometry Homework

In this right angles worksheet, students use trigonometric ratios to determine the length of a missing side or a missing angle of a right triangle. This two-page worksheet contains 19 problems.

Lesson Planet

#### Pythagorean Theorem

In this Pythagorean theorem worksheet, students use the Pythagorean theorem to find the length of a missing side of a right triangle. This two--page worksheet contains 15 problems.

Lesson Planet

#### Hopewell Geometry

Right triangles from 2,000 years ago? Learners investigate different right triangles found in the earthworks of the Hopewell people, a Native American culture that populated the United States from 200BC to AD 500. Learners apply concepts...

Lesson Planet

#### Trigonometry

In this geometry worksheet, 10th graders solve problems that are based on the right triangle trigonometry and the special right triangles. The three page worksheet contains twelve questions. Answers are not included.

Lesson Planet

#### Right Triangle Relationships

Work with sine and cosine relationships three ways. Three questions assess pupils' understanding of the trigonometric relationship between complementary angles. Learners use the value of one ratio to determine the other and the equal...

Lesson Planet

#### Right Triangle Applications: Lesson 3

Find the connection between trigonometry and tornadoes. Pairs investigate a tornado in Joplin, Mo., and use trigonometry to find its size. The pupils determine the path of the tornado and find the distance needed to travel to help...

Lesson Planet

#### Investigating Special Right Triangles

Scholars first investigate relationships in the side lengths of 30°-60°-90° triangles and 45°-45°-90° triangles. This knowledge then helps them solve problems later in the lesson about special right triangles.

Lesson Planet

#### Refiguring Pythagoras

Why was Pythagoras so obsessed with squares? The assessment task posits the question of whether the geometric interpretation of the Pythagorean Theorem holds for figures other than squares. Scholars first consider the case of semicircles...

Lesson Planet

#### Central Valley Math Project

Middle schoolers study the Pythagorean Theorem. They describe what it means to square a number. Pupilsuse the Pythagorean Theorem to prove the sides of given triangles, and use geometric pieces of paper to create a right triangle and...

Lesson Planet

#### Vectors

In this vectors learning exercise, 10th graders solve and complete 7 various types of problems related to vectors. First, they find the third side and the angle labeled in each right triangle. Then, students resolve each of the vectors...

Lesson Planet

#### Easy Worksheet: Trigonometry

In this trigonometry worksheet, students solve 4 short answer problems. Students find the sine, cosecant, secant or cotangent of an angle given a diagram of a right triangle with various measurements labeled.

Lesson Planet

#### Circles Review

In this circle learning exercise, 10th graders solve and complete 25 various types of problems that include measuring various circles. First, they determine the measure of a diameter in a given circle. Then, students determine the length...

Lesson Planet

#### Basic Trigonometry ll

Sal continues with examples of finding the sine, cosine, and tangent of an angle in a right triangle using SOH-CAH-TOA. In his examples, he reviews the use of the Pythagorean Theorem and rationalizing the denominator of a fraction. He...

Lesson Planet

#### Tangram Project

Tangrams make geometry tangible for students of all levels, and are an instructional favorite from elementary school on. In this high school lesson, however, the basic premises of tangram combinations are extended to an investigation of...

Lesson Planet

#### 30-60-90 Triangles All

Using this video, which is the fourth in a series, the instructor continues a discussion involving the Pythagorean theorem. This video focuses on calculations involving right triangles with 30 and 60 degree angles.

Lesson Planet

#### Trig Cheat Sheet

Your pre-calculus learners will make use of this wonderful cheat sheet that summarizes all things trigonometric. Definitions based on both the unit circle and the right triangle are included, as well as many convenient trigonometric...

Lesson Planet

#### What is the Pythagorean Theorem?

Need to find the length of a side of a right triangle? Just use the Pythagorean Theorem! Follow along as the tutor defines the Theorem, explains how it works, then uses it to determine the missing length of a right triangle.

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#### Triangle Area

While the lesson focuses on right triangles, this activity offers a great way to practice the area of all triangles through an interactive webpage. The activity begins with the class taking a square paper and cutting in in half; can they...

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#### Geometric Mean and Congruent Right Triangle

Students investigate right triangles using the six trigonometric identities. In this geometry lesson, students examine why the altitude in a right triangle creates two or more right triangles.

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#### Special Right Triangles

Students calculate different parts of a right triangle. In this algebra lesson, students use the Pythagorean Theorem and the similarity and congruent theorems to solve triangular problems.

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#### Trigonometric Functions of Acute Right Triangles

Young scholars derive the six trigonometric functions. For this trigonometry lesson, students show their understanding of trigonometric functions as they relate the right triangles. They find the missing angles and side use trig ratios...

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#### Rational Equations

Algebra and geometry learners have room to show their work on this worksheet that includes solving rational equations and right triangle trigonometric equations. A knowledge of solving linear and quadratic equations is a prerequisite to...

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#### Right Triangles

In this right triangles worksheet, 10th graders solve and complete 12 various types of problems. First, they solve for x given each of the right triangles shown. Then, students determine the length of the shorter diagonal given the...

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#### Right Triangles and Geometer's Sketchpad

Eighth graders use Geometer's Sketchpad to construct squares on a 4 quadrant coordinate system which will form right triangles. Using the Geometer's Sketchpad, student discover relationship of the Pythagorean Theorem as they compare the...

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#### Right Triangles

For this right triangles worksheet, 10th graders solve 10 different problems that include various right triangles. First, they find the value of a base given its hypotenuse. Then, students determine an angle given the perimeter and...

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#### Special Right Triangles

In this special right triangles instructional activity, students solve 15 short answer problems. Students use trigonometric functions to find missing side lengths of various right triangles.

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#### Right Triangles

In this right triangles worksheet, 10th graders solve and complete 5 different types of problems. First, they solve each of the right triangles shown and express each answer correct to two decimal places. Then students find the...

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#### Special Right Triangles Homework

In this geometry worksheet, students solve both kinds of special right triangles. There are 12 questions with multiple parts.

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#### Discover the Pythagorean Theorem

Students explore the Pythagoras theorem. In this geometry lesson, students make right triangles and identify the parts of the triangle. Students complete measurements of the sides of the triangle.

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#### Right Triangles

In this right triangles worksheet, 10th graders solve and complete 5 various types of problems. First, they solve each of the triangles shown and find the area of each triangle. Then, students find the perimeter and area of the regular...

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#### Right Triangles

In this right triangles learning exercise, 10th graders solve and complete 13 different problems. First, they find the lengths of both missing sides. Then, students find the altitude of an equilateral triangle given the measure of one...

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#### Easy Worksheet: Right Triangles and Circles

For this right triangles and circles worksheet, students solve 4 short answer problems. Students describe a right triangle formed by point on a circle and an angle measure.

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#### Right Triangles

In this right triangles worksheet, students solve and complete 19 different problems. First, they find the missing length using the diagram shown. Then, students find the length in the code at the bottom and write the letter of the...

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#### The Pythagorean Theorem

In this Pythagorean theorem worksheet, 9th graders solve and complete 8 different problems that include using the Pythagorean theorem to solve. First, they find the missing measure in each right triangle. Then, students make a drawing...

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#### The Tangent Ratio

Young scholars use the tangent ratio to determine the height and base length of a right triangle. In this using the tangent ratio to determine the height and base length of a right triangle lesson plan, students construct a right...

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#### Geometric Mean and the Pythagorean Theorem

In this geometric mean and Pythagorean Theorem worksheet, 10th graders solve 9 problems related to determining the geometric mean by applying the Pythagorean Theorem in each problem. First, they find the geometric mean between each pair...

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#### Pythagorean Theorem Worksheet

In this online math instructional activity, students use the Pythagorean Theorem to determine if given triangles are "right" triangles. This excellent resource allows the students to check their answers, and to get "hints" should they...

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#### Pythagorean Theorem

Students apply properties of Pythagorean to solve problems. In this geometry lesson, students identify the different parts of a right triangle using ratios. they solve problems using squares and square roots.

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#### Pythagorean Theorem Homework

In this Pythagorean theorem instructional activity, learners determine if given side lengths for right triangles, find the length of the missing side in right triangles, and find the length of the diagonals formed in boxes given side...

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#### The Pythagorean Theorem

In this Pythagorean theorem worksheet, 9th graders solve and complete 16 different problems that include using the Pythagorean theorem to solve each one. First, they find each missing measure given the hypotenuse of a right triangle....

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#### Mean Twisters - Mean Proportional

In this mean proportional worksheet, students work in pairs to solve right triangle problems. They use ratios and proportions of similar triangles to determine a missing length. This two-page worksheet contains 16 problems.

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#### Geometry Worksheet: Pythagoras' Theorem

In this Pythagorean Theorem worksheet, students use the Pythagorean Theorem to find the length of the unlabeled side of the right triangle. There are 8 problems all together.

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#### A Different Proof of the Law of Cosines

In this proofs worksheet, students construct 1 proof of the law of cosines. Students construct a right triangle within a circle to prove the law of cosines.

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#### Right Triangles

In this right triangles worksheet, young scholars solve and complete 2 different types of problems. First, they take the case of an isosceles right triangle with a given leg and hypotenuse. Then, students find the sum of the squares of...

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#### Solving Right Triangles

Solve that triangle! Your class examines angles and side measurements on 20 right triangles to determine the missing measurements. For some, they are given two sides while for others, they are given an angle and a side.

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#### Colorful Triangles

Learners examine a figure made up of different types of triangles and then determine whether each triangle is right, acute, or obtuse. Next, they color each type of triangle a different color. Finally, pupils answer three fill in the...

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#### CAHSEE Practice: Problems 38-42

Sal shows your students how to thoroughly and effectively read and solve math problems on the CAHSEE (and other standardized tests) in this engaging video. From masters of geometry to students who struggle with basic math skills, these...

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#### Trigonometry Review Sheet

Get the trig facts fast, and use the review sheet as a guide in the classroom. The worksheet also includes a document version if any changes are needed to the problems. The information includes a small degree/radian chart, a graph of all...

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#### Hopewell Geometry

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

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#### Circles in Triangles

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

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#### Altitude to the Hypotenuse

Gain some altitude with the geometric mean. Pupils discover the relationship between the three triangles formed by drawing the altitude to the hypotenuse in a right triangle. The lesson introduces the geometric mean and provides problems...

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#### The Pythagorean Theorem

There isn't a more popular geometry formula than the Pythagorean Theorem! Learners understand the special side relationships in a right triangle. They use the Pythagorean Theorem to find missing sides and to solve problems. They begin...

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#### Similarity and Right Triangle Trigonometry

Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...

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#### Trigonometric Ratios: A Geometer's Perspective

What do all right triangles have in common? Young mathematicians investigate the trigonometric ratios in relation to right triangles. Their investigations lead to a hypothesis they use to determine unknown lengths in different triangles.

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#### Module 5: Modeling with Geometry

Solids come in many shapes and sizes. Using geometry, scholars create two-dimensional cross-sections of various three-dimensional objects. They develop the lesson further by finding the volume of solids. The module then shifts to finding...

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#### The Pythagorean Relationship

Add up areas of squares to discover the pythagorean relationship. Small groups create right triangles with squares along each side. They calculate the areas of each square and notice the relationship. Groups construct other types of...

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#### Exact Trigonometric Ratios: Triangles to the Unit Circle

Special right triangles give special information. Individuals learn how to find trigonometric ratios in all quadrants. This involves using special right triangles and the Pythagorean Theorem.

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#### Wheel of Theodorus Extra Credit Project

Think it's possible to make a wheel out of triangles? According to this geometry project it is. Using their knowledge of the Pythagorean Theorem, young mathematicians carefully calculate and draw a series of right triangles that form...

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#### Pythagorean Theorem and Its Converse

Challenge scholars to prove the Pythagorean Theorem geometrically by using a cut-and-paste activity. They then must solve for the missing sides of right triangles.

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#### Finding Perimeter Using the Pythagorean Theorem

What would right triangles be without the Pythagorean Theorem? Here learners see how to apply the Pythagorean Theorem to finding missing sides of triangles. The examples include both right and non-right triangles.

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#### 2D Rotations of Triangles

Where does the line of rotation need to be to get a cone? Pupils respond to three questions involving rotating a right triangle about different lines. The scholars describe the solid created along with providing details about its...

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#### Module 7: Modeling with Geometry

Model good modeling practices. Young mathematicians first learn about cross sections and solids of revolution. They then turn their attention to special right triangles and to the Laws of Sine and Cosine.

EngageNY

#### Unknown Angles

How do you solve an equation like trigonometry? Learners apply their understanding of trigonometric ratios to find unknown angles in right triangles. They learn the meaning of arcsine, arccosine, and arctangent. Problems include basic...

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#### Special Triangles and the Unit Circle

Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value of...

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#### Introduction to the Pythagorean Theorem

Use a new medium to investigate an old mathematical theorem. Young mathematicians learn about the Pythagorean Theorem from a YouTube video in the Socratica Geometry playlist. They first see if a set of values is a Pythagorean triple and...

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#### Two Wheels and a Belt

Geometry gets an engineering treatment in an exercise involving a belt wrapped around two wheels of different dimensions. Along with the wheels, this belt problem connects concepts of right triangles, tangent lines, arc length, and...

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#### Pythagorean Explorer

Make sure the measurement is right. The interactive provides right triangles with a missing side measurement. Pupils use the given sides and the Pythagorean Theorem to calculate the length of the missing side. After entering the length,...

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#### Proving Slope Criteria for Parallel & Perpendicular Lines

This lesson launches with learners graphing the fourth vertex of a given rectangle, and finding the length and slope of one of its sides; and ends with learners writing a summary sheet for parallel and perpendicular lines. In between,...

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#### Geometric Mean Homework

In this geometric mean worksheet, learners find the geometric mean of given data. They examine right triangles. This one--page worksheet contains 10 problems.

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#### Triangles

In this triangles worksheet. students solve and complete 12 different problems involving various right triangles. First, they use sine, cosine and tangent to solve each problem. Then, 10th graders write an equation for each right...

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#### Finding the Missing Length of the Right Triangle and Determining if a Right Triangle

For this Pythagorean theorem worksheet, learners determine if the six sets of given lengths form right triangles. Next. students find the missing length for sixteen right triangles. The solutions are provided.

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#### The Pythagorean Theorem

Students solve problems using the Pythagorean Theorem. In this geometry instructional activity, students find the correct ratios of each right triangle. They use the ratios to find missing angles and sides of triangles.

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#### Triangle Tango: Special Right Triangles

Students investigate properties of special right triangles. In this geometry instructional activity, students use the Pythagorean Theorem to solve for missing angles and sides. They perform reflections.

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#### Exploring the Pythagorean Theorem

In this Pythagorean theorem learning exercise, 9th graders solve and complete 16 different problems that include applying the Pythagorean theorem to solve algebraic equations. First, they determine the missing side length of each...

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#### Trigonometric Ratios

In this trigonometric ratios activity, 10th graders solve 9 different problems that include determining the trigonometric ratios of each triangle. First, they determine the sides and angles of a right triangle that is shown in each...

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#### Practice B: Trigonometric Ratios

In this trigonometric ratios worksheet, students use trigonometric ratios to determine the length of one side of a triangle or the angle measurement of right triangles. They draw vectors in a coordinate plane. This three-page worksheet...

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#### Sixteen Angle Pre-calculus Trig Problems

In this angle worksheet, students solve ten multiple choice and six free response questions. These precalculus questions cover angles, radians, and right triangles.

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#### The Pythagorean Theorem

Students read the history of the Pythagorean Theorem online and answer questions. In this right triangle lesson, students read about the Babylonians and relate them to the origin of the Pythagorean Theorem. They solve problems by...

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#### Applying the Pythagorean Theorem

For this Pythagorean theorem worksheet, 9th graders solve and complete 17 different problems that include applying the Pythagorean theorem to each situation. First, they find the length of the third side to the nearest tenth of a unit...

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#### You Can't Go Wrong with a Right Triangle 2

Upper graders use the properties of right angle trignonmetry to measure objects such as the school flagpole. They solve real world problems using these properties.

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#### Right Triangles and Proportions

In this right triangle worksheet, students identify parts of a right triangle. They find the geometric mean of given numbers and solve proportion problems. Students write similarity statements concerning triangles and find the length of...

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#### Area of Triangles Non-Right Triangles

In this geometry worksheet, students draw non-right triangles with the defined area on a provided Geoboard image. There are 16 questions.

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#### Trigonometry and Right Triangles

In this trigonometry and right triangles worksheet, students solve and complete 12 different problems that include various right triangles. First, they write the trigonometric equation, using cosine, for each right triangle shown. Then,...

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#### Right Triangles

For this right triangles worksheet, 10th graders solve various and complete 57 various types of problems. First, they find a tangent point as a fraction in simplified form and as a decimal. Then, students write two equation to use to...

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#### Right Triangles

In this right triangles instructional activity, 10th graders solve and complete 42 different types of problems. First, they find the square root and length of the hypotenuse. Then, students find the missing side length of the right...

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#### Are These Right?

Is that a right triangle or a wrong triangle? Young mathematicians look at eleven different shapes and use a measuring tool of their choice to determine which triangles have right angles. Consider cutting out sets of the shapes to...

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#### Pythagorean Theorem, Revisited

Transform your pupils into mathematicians as they learn to prove the popular Pythagorean Theorem. The 16th instructional activity in the series of 25 continues by teaching learners how to develop a proof. It shows how to prove the...

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#### Same Base and Height, Variation 2

This is a good model for learners to visualize triangles of the same base and height. They can can begin to comprehend that these triangles will have the same area no matter how the triangle is drawn. It is part of a series of resources...

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#### 30-60-90 Triangles

Half of an equilateral triangle is a special right triangle. A video instructor shows how to find the pattern of the side lengths for a 30-60-90 triangle. She then applies the relationship to different examples.