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Defining Gravity
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Lesson Planet
Mathematics Vision Project: Interactive Applets
Ready, set, go! The Mathematics Vision Project provides a collection of 10 Interactive Applets that follow the progression of learning—to practice, develop, and solidify understanding. The interactives use engaging materials that include...
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EngageNY Geometry Module 1: Congruence, Proof, and Constructions
The 36 lessons in the Geometry Module 1 collection address transformations in teaching geometry brought on by Common Core. The focus here is on transformations and the relationships between transformations and congruence. Teacher...
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Proof That Geometry Isn't Difficult
Prove that Geometry can be challenging in a good way with a wide-ranging collection of resources on proofs. The topics focus on the main skills while young mathematicians to think outside the box.
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The Trapezoid
Enjoy this nicely organized worksheet that puts together multiple problems regarding trapezoid proofs. The resource can be used as a guide that begins with proving properties and ends with solving for measures of line segments.
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Inequalities in a Triangle
Stuck with triangle proofs? Take a 180° and provide learners with a guided activity that tests their knowledge with triangle inequalities. The questions require different types of proofs that range in levels of difficulty.
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Geometry Definitions
Geometry is full of shapes, figures, and corresponding things here and there. The guide shares all of the key pieces of geometric information in a nicely color-coded and labeled sheet.
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Reasons for Geometric Statement/Reason Proofs
Stuck trying to remember the formal language of a geometric proof? Never fear, this handout has them all ready to go. The reasons are sectioned by topic so this handy guide is ready when you are to tackle those two column proofs.
EngageNY
Congruence, Proof, and Constructions
This amazingly extensive unit covers a wealth of geometric ground, ranging from constructions to angle properties, triangle theorems, rigid transformations, and fundamentals of formal proofs. Each of the almost-forty lessons is broken...
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Parallel Lines Task
Transform the classroom into a coordinate plane. Scholars walk along parallel lines drawn on a coordinate plane on the classroom floor. They measure angles and slopes and use the results to develop criteria that would make the lines...
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Parallel Lines Cut By a Transversal
Perhaps planning a city isn't so difficult after all. Scholars first perform geometric constructions and investigate how parallel lines are useful in real-world situations. They then work on a city design project, drawing street maps,...
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Parallel Lines Cut by a Transversal
Use the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...
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Real Life Parallels
There's no parallel to a great resource. Scholars take part in three lessons in which they investigate parallel lines in real-world situations. They search for and take pictures of parallel lines in and around the school, develop artwork...
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Smarter Balanced Sample Items: High School Math – Claim 3
Communication is the key. A presentation provides 25 sample items for Claim 3, Communicating Reasoning, for the Smarter Balanced High School Math assessment. Items require pupils to answer the question and provide logical reasoning to...
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Module 3: Geometric Figures
It's just not enough to know that something is true. Part of a MVP Geometry unit teaches young mathematicians how to write flow proofs and two-column proofs for conjectures involving lines, angles, and triangles.
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Soccer Angles
Yes, knowing math can make you better at sports. Small groups solve a problem involving soccer players passing a ball to score a goal. Successful solutions to the problem require using knowledge of lines and angles.
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What's Your Angle?
Explore angle relationships with a hands-on activity. Young mathematicians begin by drawing parallel lines cut by a transversal and measuring the angle pairs. After establishing the angle pairs, individuals show their understanding by...
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Transparent Transversals
Parallel lines and transversals work together to create unique angle pairs. An inquiry-based activity allows scholars to explore these relationships and give them each a name. Flashcards allow them to study the new vocabulary.
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Bank Shot
Bank on geometry to line up the shot. The resource asks the class to determine the location to bank a cue ball in a game of billiards. Using their knowledge, class members determine where to hit the bumper to make a shot and discuss...
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Perpendicular Bisectors: Lesson
Get right up and split it in half. Using a diagram, the video provides the definition of a perpendicular bisector. The portion in a playlist on basic geometry explains perpendicular bisector of a segment and of triangle sides properties.
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Angle Bisectors: Lesson
Apply bisectors and distances to angles. Using the definition of an angle bisector, a portion of a geometry playlist draws a diagram showing the angle bisector. The video details properties of an angle bisector and their converses....
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Exterior Angles Theorems: Lesson
Use the inside to find the outside. The resource presents two theorems dealing with exterior angles of a triangle. Using the two theorems, the segment from a larger geometry playlist works problems to solve for angle measures.
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Triangle Sum Theorem: Lesson
The measures all add up. The presentation, part of a helpful playlist on geometry, provides the statement of the Triangle Sum Theorem. Using the theorem, the video shows how to find the missing measure of an angle.
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Congruent Angles and Bisectors: Lesson
How is congruence shown? Using angles, the resource introduces the congruence symbol and explains the meaning of being congruent. A segment of a larger playlist on basic geometry discusses bisection as a way to arrive at two congruent...
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Same Side Interior Angles: Lesson
Supplement your scholars' knowledge of angles involved with parallel lines. Using the properties of alternate interior angles and linear pairs, the presenter shows interior angles located on the same side of a transversal of parallel...
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Alternate Exterior Angles: Lesson
Use an alternate approach to parallel lines. A resource in a comprehensive playlist on basic geometry develops the concept of alternate exterior angles and parallel lines. The presentation demonstrates how to identify alternate exterior...
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Alternate Interior Angles: Lesson
Concepts of alternate interior angles parallel the concepts of corresponding angles. Using a diagram, the presentation defines and identifies alternate interior angles formed by a transversal and two parallel lines. The video in a...
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Corresponding Angles: Lesson
Take a parallel view of correspondence. The resource, part of a playlist on basic geometry, introduces the corresponding angle postulate. By first identifying corresponding angles, the video highlights the relationship between the angle...
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Perpendicular Lines: Lesson
Perpendicular lines are all right. Using the definition of perpendicular, the video lesson introduces perpendicular lines.The portion a basic geometry playlist makes connections between the rules of parallel lines and perpendicular lines.
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Parallel and Skew Lines: Lesson
Is it possible for a pair to be parallel and skew? The resource provides the class opportunities to find out by examining the properties of parallel and skew lines. Part of a playlist on basic geometry, the video includes a brief...
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Engineering Design Challenge: Exploring Structures in High School Geometry
Applying their knowledge of theorems about lines, angles, and triangles, groups build a toothpick and stick bridge to support their text book. The teams use the design process to plan, build, test, and refine their bridge designs. The...
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Determination of the Optimal Point
Meet at the Fermat-Torricelli point. Individuals determine the optimal location of a facility given criteria. This means they must consider points of concurrency in a triangle, including the centroid, the incenter, the circumcenter, the...
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Conjectures and Proof
Transform proofs using triangle rotations. By rotating a triangle around various points, class members develop proofs. Participants prove relationships of alternative interior angles formed by parallel lines and the sum of the interior...
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Identify Line Types: Intersecting and Parallel Lines
Navigate your way through a lesson on types of lines. Individuals drag line segments to illustrate paths between pairs of houses on an interactive map. They determine if these line segment pairs are intersecting or
parallel.
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Identify Line Types: Identify Types of Lines
If lines aren't parallel or perpendicular, then what are they? An interactive lets users rotate a line to change its orientation
with respect to another line. It then indicates whether the
lines are parallel, perpendicular, or...
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Accurately Acquired Angles
From any angle, the resource on proving angle relationships is a good one to use. Scholars first engage in activities that enable them to identify types of angles when a transversal cuts two parallel lines. In groups, they prove a...
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Name That Triangle
Given a line segment and its perpendicular bisector, pupils visualize a triangle with the endpoints and a point on the perpendicular as its vertices. Learners determine the type of triangle formed and provide a justification for the...
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Proving the Vertical Angles Theorem
Why are vertical angles congruent? Pupils must identify a pair of congruent vertical angles from a diagrams. Of course, they must prove that they are congruent.
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Proof with Parallelogram Vertices
Geometric figures are perfect to use for proofs. Scholars prove conjectures about whether given points lie on a triangle and about midpoints. They use a provided dialogue among fictional learners to frame their responses.
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Proving the Alternate Interior Angles Theorem
Proofs not included; you must write them on you own. Learners write a proof that alternate interior angles are congruent. The proof must rely on rigid motions.
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Finding Angle Measures 1
How does your class measure up to finding angle measurements? Young scholars of geometry find the measurements of four missing angles on three concurrent lines. After finding each measurement, they must then justify their answers. Use...
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Finding Angle Measures 2
Can your pupils determine the measurement of seven angles from the measurement of just one? Geometry enthusiasts tackle this task in a problem involving parallel lines with a transversal. After finding the correct measurements, the class...
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Equidistant Points
What's so special about perpendicular bisectors? Pupils investigate points on the perpendicular bisector of a line segment. They write a proof for why a point on the perpendicular bisector is equidistant from the endpoints of the line...
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Finding Angle Measures 3
Is your class up to the challenge of angle measurement? Find out using a fun formative! Geometry scholars show off their skills using a simple worksheet involving parallel lines, transversals, and missing measurements. Check up on those...
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Lines and Angles
Explore angle relationships associated with transversals. Pupils construct parallel lines with a transversal and find the measures of the angles formed. They figure out how the different angles are related before constructing...
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Angles: Parallel Lines
Viewers are presented with seven problems with parallel lines and angle relationships and must use the given information to find the measures of specific angles. To finish, they explain their process in finding the measures in the problems.
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Quadrilaterals
What figure is formed by connecting the midpoints of the sides of a quadrilateral? The geometry assessment task has class members work through the process of determining the figure inscribed in a quadrilateral. Pupils use geometric...
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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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Parallel Lines, Transversals, and Angles: What’s the Connection?
Streets, bridges, and intersections, oh my! Parallel lines and transversals are a present in the world around us. Learners begin by discovering the relationship of the angles formed by parallel lines and a transversal. They then apply...
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Evaluating Statements About Length and Area
Class members complete an assessment task by identifying whether statements about triangles and quadrilaterals are always true, sometimes true, or never true. They then participate in a sorting activity with the same objective.
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Angles Formed by Transversals of Coplanar Lines
Create a strong understanding of the relationships formed when parallel lines intersect a transversal. Discuss each type of angle pair and their relationship to each other.
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Polygon Angle Sum
Using patterns to build a formula is an important mathematical skill. Pupils discover a formula to find the sum of interior angles in a polygon by analyzing a pattern. The additional videos show how to use the formula to find various...
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Coordinate Proofs
How do you know you know? Prove it! The guide goes through several examples and includes a link to a video to teach learners how to work through coordinate proofs. The goal is to prove that different shapes are indeed that shape.
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Parallel and Perpendicular Lines Worksheet
Take the work out of worksheet and give young mathematicians time to practice with lines, systems of equations, and special lines. It is a great worksheet that includes questions on all the main topics of linear equations.
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Isosceles Triangles and Special Line Segments
Under which conditions can a triangle be classified as isosceles? High schoolers practice identifying isosceles triangles and special line segments, including angle bisectors, medians of triangles, and perpendicular bisectors of sides of...
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Geometry Sample Problems
I'd like to prove that this activity has a lot to offer. Seven problems using triangles and parallelograms practice the traditional method of a two-column proof. After the activity is some practice problems that show worked out solutions.
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Parallel Lines Proofs Practice
Here is a activity that lines up perfectly with the skills needed to finish a geometric proof. Eleven problems are given to see if learners can prove that lines are parallel or angles are congruent.
EngageNY
End-of-Module Assessment Task - Geometry (module 1)
Have you hit a wall when trying to create performance task questions? Several open-ended response questions require a deep level of thinking. Topics include triangle congruence, quadrilaterals, special segments, constructions, and...
EngageNY
Review of the Assumptions (part 2)
Is the amount of information getting overwhelming for your geometry classes? Use this strategy as a way to organize information. The resource provides a handout of information studied in relation to triangle congruence. It includes a...
EngageNY
Special Lines in Triangles (part 2)
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
EngageNY
Review of the Assumptions (part 1)
What was the property again? Tired of hearing this from your pupils? Use this table to organize properties studied and as a reference tool for individuals. Learners apply each property in the third column of the table to ensure their...
EngageNY
Special Lines in Triangles (part 1)
Allow your pupils to become the mathematicians! Individuals explore the properties of a midsegment of a triangle through construction and measurement. Once they figure out the properties, learners use them to draw conclusions.
EngageNY
Properties of Parallelograms
Everyone knows that opposite sides of a parallelogram are congruent, but can you prove it? Challenge pupils to use triangle congruence to prove properties of quadrilaterals. Learners complete formal two-column proofs before moving on to...
EngageNY
Mid-Module Assessment Task - Geometry (Module 1)
How do you prepare class members for the analytical thinking they will need in the real world? An assessment requires the higher order thinking they need to be successful. The module focuses on the concept of rigid transformations...
EngageNY
Unknown Angle Proofs—Proofs of Known Facts
Lead the class in a Greek history lesson with a geometric twist. Pupils relate a short video about geometric properties to modern-day methods of solving for unknown angles. They discuss parallel line theorems and complete practice...
EngageNY
Unknown Angle Proofs—Proofs with Constructions
Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...
EngageNY
Unknown Angle Proofs—Writing Proofs
What do Sherlock Holmes and geometry have in common? Why, it is a matter of deductive reasoning as the class learns how to justify each step of a problem. Pupils then present a known fact to ensure that their decision is correct.
EngageNY
Solve for Unknown Angles—Angles in a Triangle
Assist your class with each angle of geometry as they use exterior angles to form linear pairs with adjacent interior angles. They cover multiple vocabulary terms and work practice problems, complete with justifications, before taking an...
EngageNY
Solve for Unknown Angles—Transversals
Lead your class on an exciting journey through the world of math as they review geometry facts and solve for unknown angles. They learn how to use auxiliary lines and congruent angles to correctly complete each practice problem...
EngageNY
Solve for Unknown Angles—Angles and Lines at a Point
How do you solve for an unknown angle? In this sixth installment of a 36-part series, young mathematicians use concepts learned in middle school geometry to set up and solve linear equations to find angle measures.
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Postulates and Proofs: Let's take it to the courtroom!
Order in the court! Turn your geometry classroom into a courtroom and have your pupils defend their proofs. A fun and educational lesson allows both individual and group work with geometric proofs and group presentations in a court of...
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Analytic Geometry Study Guide
Are you looking for a comprehensive review that addresses the Common Core standards for geometry? This is it! Instruction and practice problems built specifically for standards are included. The material includes geometry topics from...
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Company Logo
Modern advertising takes a geometric turn with this unit. The final assessment activity leads pupils through the logical analysis of a fictional logo, including the development of a paragraph proof. The wealth of resources leading up to...
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Accelerated Geometry Review Sheet
Your geometry learners use their knowledge of various geometric concepts to write proofs. Starting with givens containing parallel line segments with transversals and triangles and quadrilaterals, and the mid-point and distance formulas;...
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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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Geometric Figures
Logical thinking is at the forefront of this jam-packed lesson, with young mathematicians not only investigating geometric concepts but also how they "know what they know". Through each activity and worksheet, learners wrestle with...
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Reflections and Equilateral Triangles II
Given the lines of symmetry in an equilateral triangle, your learners find where the pre-image vertices are mapped onto the new image. They explore the properties of equilateral triangles, the impact of reflections, and the idea that the...
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Reflections and Equilateral Triangles
Your learners collaboratively find the lines of symmetry in an equilateral triangle using rigid transformations and symmetry. Through congruence proofs they show that they understand congruence in terms of rigid motions as they prove...
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Tangent Lines and the Radius of a Circle
Your Geometry learners will collaboratively prove that the tangent line of a circle is perpendicular to the radius of the circle. A deliberately sparse introduction allows for a variety of approaches to find a solution.
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Vertical Angles Proof Samples
This visual, manipulative-based format for teaching geometric proofs nicely scafolds learners' development of mathematical reasoning and proof skills. This sample represents a proof of the congruence of vertical angles in four formats;...
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Manufacturing: Gas Metal Arc Welding (GMAW) Shielding Gas Mix
Middle schoolers apply math to the real-world skill of choosing the correct shielding gas mixture for welding. Even if you do not have shielding gas cylinders on hand for demonstrating, the concepts of converting percentages into...
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Architecture and Construction: Stair Construction
Within the context of the construction industry, algebra pros begin to calculate slope from the sizes of stair steps. This is a terrific instructional activity, especially for aspiring engineers. Just be aware that it might be a stretch...
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Is This a Rectangle?
How do you show that something is a rectangle? This activity starts with four coordinate points and asks young geometers to explain whether they create a rectangle. Knowledge from both geometry and algebra come into play here, as well...
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Sailing with Congruency
Young geometers will have fun with this real-world application of a geometry theorem. Working in groups, they explore the design of sailboats and must come up with a convincing argument about how the manufacturer can save time and money....
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Points equidistant from two points in the plane
Young geometers apply their deductive reasoning skills and knowledge of proving triangles congruent in a task that asks them to prove if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints...
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Meet Me at the Corner
Geometers use their knowledge of vertical, alternate interior, and corresponding angles in a real-world activity. Engineers plan to install guard rails at dangerous intersections of a city and need to know the angle at which to construct...
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The Parallelogram Law
Use your pupils' sense of curiosity to explore the Parallelogram Law. Here is an activity that outlines a complete lesson from beginning to end, allowing pupils to follow a conjecture through to the proof stage.
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Health Science: Back to Basics
This lesson focuses on unit conversion, proportions, ratios, exponents, and the metric system. Discuss measurement with your math class and demonstrate how to solve several health-science word problems. Give learners a chance to visit an...
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Nested Similar Triangles
Nested triangles have been created so that they share a common vertex and vertex angle. Learners drag the endpoints of the side that is opposite the common angle to discover the conditions that make the nested triangles similar. When...
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Alternate Interior Angles
Label angles of parallel lines to analyze the angles created by a transversal and two parallel lines. They graph their lines and observe the similarity and difference in the angles.
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Creating Parallel Lines and Transversals
Have your class create parallel lines. Students will learn how to identify the different angles created by a parallel line cut by a transversal. Then, they identify and name similar and different angles.
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Vertical Angle Proofs
Using inductive and deductive reasoning, geometers prove vertical angles are congruent. They use patty paper to construct and measure vertical angles. Then they prove corresponding angles are congruent and consider other conjectures.
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Betweenness and the Sum of Parts
High schoolers differentiate lines and angles using betweenness in this geometry lesson. They differentiate angles and lines using Cabri Jr. and analyze the data and make conjecture.
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Proving Angles Congruent and Developing Proofs
Students explore the concept of angles. In this angles lesson, students determine the relationships of vertical, complementary, supplementary, and adjacent angles. Students construct proofs using their Ti-Nspire about vertical angles...
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Shortest Distance Between Points and Lines
Learners use technology to determine the shortest between two points in a plane. They are required to support their analytic explanations with visual illustrations.
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Angles and Transversals
Pupils explore the concept of angles and transversals. They construct parallel and non-parallel lines cut by a transversal using Cabri Jr. Learners then determine which angles are congruent and the relationship of angles when two lines...
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Angles Formed By Parallel Lines
Young scholars explore the concept of angles formed by parallel lines.They graph two parallel lines cut by a transversal, then measure the angles formed by the transversal and record the data in a table. Learners make conjectures about...