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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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 a² + b² = c² then the triangle is a right triangle.
If the side lengths of a triangle a, b, c, do not satisfy a² + b² = c², 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 a² + b² = c²
• This theorem has a converse:
If the lengths of three sides of a triangle, a, b, and c, satisfy c² = a² + b², 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.