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 1. 2. x 12 10 x-3 4 x+6 x+1 x

Section 8-5 Similarity Theorems

1. Find x 40 36 65 x

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

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.

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

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.

4. Solve for x 12 5 x 4 9 7

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.

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

 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

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

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