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8-1Similarity in Right Triangles

- One Key Term
- One Theorem
- Two Corollaries

Theorem 8-1

- Altitude Similarity Theorem
- The altitude to the hypotenuse of a right

triangle divides the triangle into two triangles

that are similar to the original triangle and to

each other.

C

A

B

D

Vocabulary

- Geometric Mean

1 Finding the Geometric Mean

- Find the geometric mean of 15 and 20.

Corollary 1 to Theorem 8-1

- The length of the altitude to the hypotenuse of

a right triangle is the geometric mean of the

lengths of the segments of the hypotenuse.

C

A

B

D

Corollary 2 to Theorem 8-1

- The altitude to the hypotenuse of a right

triangle separates the hypotenuse so that the

length of each leg of the triangle is the

geometric mean of the length of the adjacent

hypotenuse segment and the length of the

hypotenuse.

C

A

B

D

2

4

- Solve for x and y.

12

x

y

4

x

y

12

y

x

16

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