Digits, Grade 8, Volume 1, Homework Helper

4-3: The Converse of the Pythagorean Theorem

Key Concept

The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

If ΔABC is a right triangle, then a 2 + b 2 = c 2.

The converse is also true.

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

If a 2 + b 2 = c 2, then ΔABC is a right triangle.

Right triangle ABC. The length of Hypotenuse AB is c. Length AC is b. Length BC is c.

Part 1

Example Identifying Right Triangles

Decide if each of the following is a right triangle. Justify your reasoning.

  • a. A right triangle with legs of length 6 and 8 and a hypotenuse of length 10.

  • b. A right triangle with legs of length 4 and 5 and a hypotenuse of length 6.

  • c. A right triangle with legs of length 2.5 and 6 and a hypotenuse of length 6.5.

  • d. A right triangle with legs of length 4 and 7 and a hypotenuse of length 8.

Solution

Use the converse of the Pythagorean Theorem to determine whether each triangle is a right triangle.

  • a. A right triangle with legs of length 6 and 8 and a hypotenuse of length 10.

    table with 4 rows and 2 columns , row1 column 1 , , eh squared , plus , b squared , , column 2 modified modified question mark with under bar below with under bar below , , c squared , row2 column 1 , , 6 squared , plus , 8 squared , , column 2 modified modified question mark with under bar below with under bar below , , 10 squared , row3 column 1 , 36 plus 64 , column 2 modified modified question mark with under bar below with under bar below , 100 , row4 column 1 , 100 , column 2 equals 100 u 2 , end table

    Yes, the triangle is a right triangle because 62 + 82 = 102.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties