8-1 Similarity in Right Triangles

1
8-1Similarity in Right Triangles

• One Key Term
• One Theorem
• Two Corollaries

2
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
3
Vocabulary

1. Geometric Mean

4
1 Finding the Geometric Mean

• Find the geometric mean of 15 and 20.

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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
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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
7
2
4

• Solve for x and y.

12
x
y
4
x
y
12
y
x
16