Core Connections Geometry, 2013
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Core Connections Geometry, 2013 View details
2. Section 12.2
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Exercise 63 Page 753

Practice makes perfect
a 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=12, b=12, and c=12 into a^2+b^2=c^2, and see if they produce a true statement.
a^2+b^2=c^2
12^2+ 12^2? = 12^2
144+144 ? =144
288≠ 144 *
The values produce a false statement, so the described triangle is not a right triangle.
b 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=5, b=12, and c=13 into a^2+b^2=c^2, and see if they produce a true statement.
a^2+b^2=c^2
5^2+ 12^2? = 13^2
25+144 ? =169
169=169 âś“
The values produce a true statement, so the described triangle is a right triangle.