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84 Similarity in Right Triangles

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The altitude to the hypotenuse of a right triangle divides the triangle into two ... the length of the adjacent hypotenuse segment and the length of the hypotenuse. ... – PowerPoint PPT presentation

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Title: 84 Similarity in Right Triangles


1
8-4Similarity in Right Triangles
  • One Key Term
  • One Theorem
  • Two Corollaries

2
Theorem 8-3
  • 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
  • Geometric Mean

4
1 Finding the Geometric Mean
  • Find the geometric mean of 15 and 20.

5
Corollary 1 to Theorem 8-3
  • 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
6
Corollary 2 to Theorem 8-3
  • 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
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