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Understanding Indirect Measurement & Similarity Theorems in Geometry

This resource explores indirect measurement and additional similarity theorems in geometry, focusing on the proportional relationships between triangles. Key concepts include proportional altitudes, medians, and angle bisectors in similar triangles. Detailed examples demonstrate how to solve for unknown variables (x) using provided ratios. Students will learn to estimate measurements, like the width of a lake, and gain practice through various problems designed to enhance their understanding of these critical geometric principles.

amery-hendricks
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Understanding Indirect Measurement & Similarity Theorems in Geometry

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

  2. Section 8-5 Similarity Theorems

  3. 1. Find x 40 36 65 x

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

  5. 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 x 6 4 9 6 5.25 x

  7. 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 x 5 4 9 7

  9. 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. 105  40x = 7875  x = 196.9 = x 40 75 8.5 Indirect Measurement and Additional Similarity Theorems 5. Estimate the width of the lake.

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

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

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

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