EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
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 lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
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
Unknown Angle Problems with Inscribed Angles in Circles
We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson then...
Virginia Department of Education
Pythagorean Theorem
Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.
EngageNY
Are All Parabolas Congruent?
Augment a unit on parabolas with an instructive math activity. Pupils graph parabolas by examining the relationship between the focus and directrix.
Curated OER
Pythagorean Theorem by Graphic Manipulation
There are many different ways to show a proof of the Pythagorean Theorem. Here is a nice hands-on paper cutting activity that shows a graphic representation. You can even challenge your young Pythagoreans to come up with their own...
Curated OER
Two Column Logic Proofs
Students complete two column proofs. In this geometry lesson,students derive the reasons their answers are correct using logic. They write the proof step by step using two columns.
Curated OER
Proofs with Triangles
In this geometry worksheet, student solve problems with triangles using proofs. They identify the solution based on SSS, SAS, ASA. There are 5 proofs tobe completed.
Curated OER
Coordinate Proofs
Students explore the concept of coordinate proofs. In this coordinate proofs lesson plan, students write coordinate proofs using properties of distance, slope, and midpoint. Students discuss why it is sometimes beneficial to double the...
Curated OER
The Premises of Geometry
In this geometry worksheet, students solve for missing midpoints, segments and angles using algebraic equations. They use geometric properties to solve these equations. There are 32 questions on 7 different worksheets.
Curated OER
Pythagorean Theorem Proof
Tenth graders investigate the Pythagorean Theorem. Then they type up a formal paragraph proof of a proof of their choice.
Curated OER
History / Introduction of Pythagorean Theorem
Learners explore Pythagoras and the history behind his theorem. They work together to solve a proof that is embedded in the lesson.
Curated OER
Proving Quadrilateral Properties
Working backwards can sometimes help you see a path to solving a problem. In this chapter, properites of quadrilaterials are proven by looking at flowcharts and working the probem backwards. Worked through examples are given, along with...
EngageNY
The Inscribed Angle Alternate – A Tangent Angle
You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their newfound...
Curated OER
Proving the Pythagorean Theorem
Students solve problems using the pythagorean Theorem. In this geometry lesson, students complete proofs using the Pythagorean Theorem. They share their proofs and solutions with their classmates and family members.
Curated OER
Inequalities and Triangles
Students prove and apply theorems of triangle inequality and hinge theorem. In this geometry activity, students will discuss which triangle is bigger and why. They will use theorems, such as Exterior Angle Inequality or the Pythagorean...
Curated OER
Around the World With Geometry
Learners identify shapes, create shapes, and make a pyramid, a drum, and a sail using their shapes. In this shapes lesson plan, students also identify plane and space shapes.
West Contra Costa Unified School District
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 plan about special right triangles.
EngageNY
Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
Shodor Education Foundation
Cross Sections
Use this activity on cross-sections of three-dimensional shapes in your math class to work on algebra or geometry Common Core standards. The lesson includes a list of relevent terminology, and a step-by-step process to illustrate the...
Alabama Learning Exchange
Triangle Area: No Height? Use the Sine
No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.
EngageNY
Three-Dimensional Space
How do 2-D properties relate in 3-D? Lead the class in a discussion on how to draw and see relationships of lines and planes in three dimensions. The ability to see these relationships is critical to the further study of volume and other...
EngageNY
How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.