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Chapter 4 – Scale Factors and Similarity Key Terms

Chapter 4 – Scale Factors and Similarity Key Terms. Corresponding Angles – Angles that have the same relative position in two geometric figures Corresponding Sides – Sides that have the same relative position in two geometric figures

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Chapter 4 – Scale Factors and Similarity Key Terms

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  1. Chapter 4 – Scale Factors and Similarity Key Terms • Corresponding Angles– Angles that have the same relative position in two geometric figures • Corresponding Sides– Sides that have the same relative position in two geometric figures • Similar – have the same shape but different size and have equal corresponding angles and proportional corresponding sides.

  2. 4.3 Similar Triangles Learning Outcome: To be able to identify similar triangles and determine if they are proportional

  3. Symbols Δ triangle ° degrees ~ similar angle

  4. Identify Similar Triangles Example 1: Determine if ∆ABC is similar to ∆EFG. 12 A B 4 E F 3 9 G C Similar triangles have corresponding angles that are equal in measure and corresponding sides that are proportional in length.

  5. Identify Similar Triangles Note: B is the same as ABC Example 1: Determine if ∆ABC is similar to ∆EFG. Side Question: What does the sum of all the angles of a triangle ALWAYS add up to? 3 Corresponding Angles are proportional with a scale factor of equal. Compare Corresponding Sides The corresponding sides are proportional with a scale factor of 3. ∆ABC is ~∆EFG Compare Corresponding Angles

  6. Show you Know – Determine if each pair of triangles is similar.

  7. Assignment • Page 150 (4-7,9,10,12-14

  8. PERIOD 1 BRING FOOD FOR THE MINGA FOOD BANK COLLECTION TOMORROW!!!

  9. 4.3 Similar Triangles Learning Outcome: To be able to solve problems involving similar triangles and find missing side lengths

  10. Use Similar Triangles to Determine a Missing Side Length K Example 2: Kyle is drawing triangles for a math puzzle. Use your knowledge of similar triangles to determine • If the triangles are similar • the missing side length 21 L T M 10.5 7 V U 8

  11. Example 2 a) If the triangles are similar K Check that ΔKLM is similar to ΔTUV. The sum of the angles in a triangle are 180°. K = 180° - 50°-85° = 45° U = 180° - 85°-45° = 45° Note: It is not necessary to prove both conditions for similarity. One is sufficient. L T M Compare corresponding Angles: 1 7 V U 8 All pairs of corresponding angles are equal. Therefore, ΔKLM ~ ΔTUV

  12. Example 2 b) the missing side length K You can compare corresponding sides to determine the scale factor. L T 3 M 1 7 The scale factor is 3. You can solve for the unknown length. V U 8

  13. Example 2 b) the missing side length K Method 1: Use a scale factor 3 x=31.5 L T M 1 7 The missing side length is 31.5 units. V U 8

  14. Example 2 b) the missing side length Since the triangles are similar, you can use equal ratios to set up a proportion. Method 1: Use a Proportion K x1.5 L T M 1 7 x=31.5 x1.5 V U 8 The missing side length is 31.5 units.

  15. Similar Triangles • Similar triangles have been multiplied by a scale factor with enlargement or reduction. Consequently, similar triangles have: • Corresponding Angles - Equal internal angles • Corresponding Sides - Proportional side lengths (because of scale factor) • Unlike polygons in general, to check if triangles are similar, checking one of the conditions above suffices. If one is true, the other follows.

  16. Show you Know – Solve using a method of your choice

  17. Assignment • Page 150 (9-14) • Due Tuesday, October 23rd

  18. Assignment • Page 150 (1-2, 5, 7-9, 13-14) • Due Friday, October 18th

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