Big Ideas Math: Modeling Real Life, Grade 8
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6. The Converse of the Pythagorean Theorem
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Exercise 9 Page 413

Yes.

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 look at the given triangle.

Let's substitute a=27meters, b=36meters, and c=45meters into a^2+b^2=c^2, and see if they produce a true statement.
a^2+b^2=c^2
27^2+ 36^2? = 45^2
729+1296 ? =2025
2025 = 2025 âś“
The values produce a true statement, so the described triangle is a right triangle.