Examples, solutions, and videos to help Grade 8 students explain a proof of the converse of the Pythagorean Theorem.and apply the theorem and its converse to solve problems.
Lesson 16 Student Outcomes
• Students explain a proof of the converse of the Pythagorean Theorem.
• Students apply the theorem and its converse to solve problems.
Lesson 16 Summary
The converse of the Pythagorean Theorem states that if a triangle with side lengths a, b, and c satisfies a 2 + b 2 = c 2 , then the triangle is a right triangle.
The converse can be proven using concepts related to congruence.
Lesson 16 Classwork
Discussion
So far you have seen three different proofs of the Pythagorean Theorem: If the lengths of the legs of a right triangle are a and b, and the length of the hypotenuse is c, then a 2 + b 2 = c 2 .
The converse of the Pythagorean Theorem:
If the lengths of three sides of a triangle, a, b, and c satisfy c 2 = a 2 + b 2 then the triangle is a right triangle, and furthermore, the side of length c is opposite the right angle.
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