+Warm Up

B

+Homework page 4 in packet

+#10

1. Given

2. Theorem 9.1

3. Given

4. Corresponding angles are congruent

5. Reflexive

6. AA Similarity

7. Transitive

+

Ch. 9.2-9.3 Pythagorean Theorem and its Converse

Students will define and apply the Pythagorean Theorem and its converse.

+Pythagorean Triple

A Pythagorean Triple is a set of three positive integers a, b, c, that satisfy the equation

.

Theorem 9.4 Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. €

c 2 = a2 + b2 a

b

c

+Converse of the Pythagorean Theorem

If the square of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

a

b

c

+Theorem 9.6

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is acute.

Theorem 9.7

If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

b

a

c

C

A

Bc2<a2+b2

ba

c

C

A

B

c2>a2+b2

Or a2+b2>c2

Or a2+b2<c2

+Practice, Practice, Practice

4. 5. 6.