1. Warm-up Solve for x 1. 2. x 12 10 x-3 4 x+6 x+1 x
8.5 Indirect Measurement and Additional Similarity Theorems
Warm-up
Solve for x x 12 10
x-3 4
x+6
x+1 x

2. Section 8-5 Similarity Theorems

3. 1. Find x 40 36 65 x

4. 2. Find x A x 75 B E 25 D C 90

5. Theorems Proportional Altitudes Theorem:
8.5 Indirect Measurement and Additional Similarity Theorems
Theorems
Proportional Altitudes Theorem:
If two triangles are similar, then their
corresponding altitudes have the same ratio as
their corresponding sides.

6. 3. Given the triangles are similar, solve for x6 4 9
5.25 6 x

7. Theorems Proportional Medians Theorem:
8.5 Indirect Measurement and Additional Similarity Theorems
Theorems
Proportional Medians Theorem:
If two triangles are similar, then their
corresponding medians have the same ratio as
their corresponding sides.

8. 4. Solve for x 12 5 x 4 9 7

9. Theorems Proportional Angle Bisectors Theorem:
8.5 Indirect Measurement and Additional Similarity Theorems
Theorems
Proportional Angle Bisectors Theorem:
If two triangles are similar, then their
corresponding angle bisectors have the same
ratio as their corresponding sides.

10. 8.5 Indirect Measurement and Additional Similarity Theorems
5. Estimate the width of the lake. x 75 =
105 40
 40x = 7875  x = 196.9

11.  12x = 72  x = 6 feet = 12 8 9 x 6. These triangles
8.5 Indirect Measurement and Additional Similarity Theorems
6. These triangles
are similar. Find x. 12 9 = 8 x
 12x = 72  x = 6 feet

12. Given angle A and angle B are right angles Prove:
8.5 Indirect Measurement and Additional Similarity Theorems
Given angle A and angle B are right angles
Prove: A B C D E

13. Assignment Page 537 # 5-20, 26, 27-33 all
write out entire proof for #27-33