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Gr. 8 Unit: 8.G.B.6-8: Understand and Apply the Pythagorean Theorem

Lesson Seed B.7: Pythagorean Proof

Essential Questions:

What are the applications of the Pythagorean Theorem and its converse?

What is the relationship among the lengths of the sides of a right triangle?

What are the properties of special right triangles and how are these properties used?

How can the Pythagorean Theorem be used to solve problems in life?

Lesson Plans and Seeds

Lesson Plan B.7: Apply the Pythagorean Theorem

Lesson Seed B.7: Pythagorean Proof

Download Seeds, Plans, and Resources (zip)

Unit Overview

Content Emphasis By Clusters in Grade 8

Progressions from Common Core State Standards in Mathematics

Send Feedback to MSDE’s Mathematics Team

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

Standard(s): 8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.

Purpose/Big Idea:

Students will use dot paper to create a visual representation for the proof of the Pythagorean theorem

Materials:

Grid paper or computer version
www.ixl.com
http://illuminations.nctm.org

Activity:
Exploration:

Draw a right triangle on your overhead/computer projector
Introduce the vocabulary of hypotenuse and legs of right triangles

Demonstrate your work on your overhead/computer projector as the students work with you on their own paper

Give each student a piece of grid paper
Draw a 3 by 4 right triangle in the middle of your grid paper
Label each leg with its length
Draw a 3 by 3 square on the leg with a length of 3 units
Draw a 4 by 4 square on the leg with a length of 4 units
What is the area of the 3 by 3 square? what is the area of the 4 by 4 square?
Extend the 4 unit leg 3 more units so it is equal to 7 units
Extend the 3 unit leg 4 more units so it is equal to 7 units
Complete a 7 by 7 square using the sides you just created
Create a 3 by 4 triangle in each corner of the 7 by 7 square
What is the area of the 7 by 7 square?
What is the area of one 3 by 4 triangle? what is the area of all four 3 by 4 triangles?
Subtract the area of the triangles from the area of the 7 by 7 square. you will have the area of the hypotenuse square.
Add the area of the 3 by 3 square and the 4 by 4 square. it should be equal the area of the hypotenuse square.
Have students summarize the relationship between the areas of the squares.
Have students work problems a through e on worksheet 1
Discuss solutions as a class
Ask students how one could find the length of a leg if one knows the length of the other leg and the hypotenuse
Work a few problems using the students' suggestions
Have students work problems a through e on worksheet 2
Discuss solutions as a class

Guiding Questions:

Ask the students to explain or show their reasoning of why the Pythagorean theorem is proven using their own unique triangle
Can this theorem be proven on triangles that are not right triangles? Explain your reasoning.

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Last Updated 3/9/2020 2:45 PM