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7.2 The Pythagorean Theorem and its Converse

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7.2 The Pythagorean Theorem and its Converse

What you’ll learn:

To use the Pythagorean Theorem

To use the converse of the Pythagorean Theorem

The Pythagorean Theorem

In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.

a²+b²=c²

A

leg

hypotenuse

b

c

C

B

a

leg

Converse of the Pythagorean Theorem

If the sum of the squares of the measures of 2 sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

If a²+b²=c²

then ABC is a right .

A

c

b

C

B

a

Pythagorean Triple – 3 whole numbers that satisfy the equation a²+b²=c².

Some common Pythagorean triples are:

3,4,57,24,258,15,179,40,41

More triples can be created by multiplying the numbers by a constant.

3,4,5 6,8,1015,20,2530,40,50

7.8

9

15.4

6

x

x

x

1.

2.

3.

17

A(2,7), B(3,6), C(-4,-1)

Determine whether each set of numbers can be the measure of the sides of a right triangle. Then state whether they form a Pythagorean Triple.

- 7, 28, 29