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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

1. The Pythagorean Theorem and Its Converse

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Exercise 25 Page 496

Use the Converse of the Pythagorean Theorem.

No, see solution.

Practice makes perfect

We are given the triangle with the lengths of its three sides, and want to determine whether it 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 a=8, b=24, and c=25 into a^2+b^2=c^2, and see if they produce a true statement.

a^2+b^2=c^2

SubstituteValues

Substitute values

8^2+ 24^2? = 25^2

Calculate power

64+576 ? =625

Add terms

640 ≠ 625

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

Subchapter links

Lesson Check p.495

Practice and Problem-Solving Exercises p.495-498

Standardized Test Prep p.498

Mixed Review p.498