body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

1. The Pythagorean Theorem

Continue to next subchapter

Exercise 5 Page 466

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 this triangle is 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 the side lengths of this triangle 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+ 22^2? = 26^2

Calculate power

196+484? =676

Add terms

680≠ 676 *

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

Subchapter links

Communicate Your Answer p.463

Monitoring Progress p.465-467

Exercises p.468-470