# Converse of the Pythagorean Theorem

Videos and solutions to help Grade 8 students learn how to apply the Pythagorean Theorem to find lengths of right triangles in two dimensions.

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Lessons for Grade 8

Common Core For Grade 8

## New York State Common Core Math Module 3, Grade 8, Lesson 14

### Lesson 14 Student Outcomes

• Students illuminate the converse of the Pythagorean Theorem through computation of examples and
counterexamples.

• Students apply the theorem and its converse to solve problems.

Lesson 14 Summary
The converse of the Pythagorean Theorem states that if side lengths of a triangle a, b, c, satisfy a

^{2} + b

^{2} = c

^{2}
then the triangle is a right triangle.

If the side lengths of a triangle a, b, c, do not satisfy a

^{2} + b

^{2} = c

^{2}, then the triangle is not a right triangle.

Classwork
Concept Development

• 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}
• This theorem has a converse:

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 is opposite the right angle.

Exercises 1 - 7

The numbers in the diagram below indicate the units of length of each side of the triangle. Is the triangle shown
below a right triangle? Show your work, and answer in a complete sentence.