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Big Ideas Math: Modeling Real Life, Grade 8 View details

6. The Converse of the Pythagorean Theorem

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Exercise 11 Page 413

Use the Converse of the Pythagorean Theorem.

No.

Practice makes perfect

We are given the lengths of the three sides of a triangle, and want to determine whether the sides form a right triangle. We will need to use the Converse of the Pythagorean Theorem.

Converse of the Pythagorean Theorem
If the sides of a triangle have lengths a, b, and c, and c^2=a^2+b^2, then the triangle is a right triangle.

This tells us that we can use the Pythagorean Theorem in reverse to test if a triangle is right. In general, the hypotenuse c has the greatest value. Let's substitute a=14millimeters, b=19millimeters, and c=23millimeters into a^2+b^2=c^2, and see if they produce a true statement.

a^2+b^2=c^2

SubstituteValues

Substitute values

14^2+ 19^2? = 23^2

CalcPow

Calculate power

196+361 ? =529

AddTerms

Add terms

557 ≠ 529 *

The values produce a false statement, so the described triangle is not a right triangle.