# Pythagorean Theorem, Revisited, Proof

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Lesson Plans and Worksheets for Grade 8
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Examples, solutions, and videos to help Grade 8 students learn how to explain a proof of the Pythagorean Theorem using similar triangles and another proof using area.

### New York State Common Core Math Grade 8, Module 7, Lesson 15

Lesson 15 Student Outcomes

• Students know that the Pythagorean Theorem can be interpreted as a statement about the areas of similar geometric figures constructed on the sides of a right triangle.
• Students explain a proof of the Pythagorean Theorem.

Lesson 15 Summary

The Pythagorean Theorem can be proven by showing that the sum of the areas of the squares constructed off of the legs of a right triangle is equal to the area of the square constructed off of the hypotenuse of the right triangle.

Lesson 15 Classwork

Discussion
This discussion is an opportunity for students to practice explaining a proof of the Pythagorean Theorem using similar triangles.
• To prove the Pythagorean Theorem, a2 + b2 = c2, use a right triangle, shown below. Begin by drawing a segment from the right angle, perpendicular to side AB through point C. Label the intersection of the segments point D.

Discussion
• Now, let’s apply this knowledge to another proof of the Pythagorean Theorem. Compare the area of similar figures drawn from each side of a right triangle.
Pythagorean Theorem proof from similar right triangles

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