Converse of the Pythagorean Theorem

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

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

Worksheets for Grade 8

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.

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