7.4 Similarity in Right Triangles

1
7.4 Similarity in Right Triangles
2
Theorem 7.3

• 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
B
A
D
3
Vocabulary

• Geometric mean - the number x such that
• , where a, b and x are positive
  numbers

4
Example

• Find the geometric mean of 4 and 18

5
Try it

• Find the geometric mean of 3 and 48

6
Corollary 1 to Theorem 7.3

• 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

7
Corollary 2 to Theorem 7.3

• 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

8
Solve for x and y
x
y
4
5
9
Answer

• Use Corollary 2 to solve for x
• Use corollary 1 to solve for y

10
Solve for x and y
4
x
12
y
11
Answer

• Use Corollary 2 to solve for x
• Use corollary 1 to solve for y

12
Classwork/Homework

• Pgs 394-395 2-22 even, 26-36 even