Exercise 54 Page 10

Use the Converse of the Pythagorean Theorem.

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=10, b=14, and c=18 into a^2+b^2=c^2, and see if they produce a true statement.

a^2+b^2=c^2

SubstituteValues

Substitute values

10^2+ 14^2? = 18^2

CalcPow

Calculate power

100+196 ? =324

AddTerms

Add terms

296≠ 324 *

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