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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. Theorem 7.4. The Pythagorean Theorem

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7 2 the pythagorean theorem and its converse

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


Theorem 7 4
Theorem 7.4

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


Theorem 7 5
Theorem 7.5

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 triples
Pythagorean Triples

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

Some common Pythagorean triples are:

3,4,5 7,24,25 8,15,17 9,40,41

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

3,4,5 6,8,10 15,20,25 30,40,50


Find x

7.8

Find x.

9

15.4

6

x

x

x

1.

2.

3.

17


Determine whether abc is a right triangle for the given vertices
Determine whether ABC is a right triangle for the given vertices.

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


Homework p 354 12 34 even quiz tomorrow on 7 1 7 2
Homework the sides of a right triangle. Then state whether they form a Pythagorean Triple.p. 35412-34 evenQuiz tomorrow on 7.1-7.2


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