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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. 4.3 Similar Triangles Learning Outcome: To be able to identify similar triangles and determine if they are proportional Symbols Δ triangle ° degrees ~ similar angle Identify Similar Triangles Example 1: Determine if ∆ABC is similar to ∆EFG. B 12 A F 9 4 E 3 G C Similar triangles have corresponding angles that are equal in measure and corresponding sides that are proportional in length. Identify Similar Triangles Note: B is the same as ABC Example 1: Determine if ∆ABC is similar to ∆EFG. 3 Corresponding Angles are proportional with a scale factor of equal. Compare Corresponding Angles ∠𝐴 = 90° 𝑎𝑛𝑑 ∠𝐸 = 90° ∠𝐵 = 37° 𝑎𝑛𝑑∠𝐹 = 37° ∠𝐶 = 53° 𝑎𝑛𝑑∠𝐺 = 53° Side Question: What does the sum of all the angles of a triangle ALWAYS add up to? Compare Corresponding Sides The 𝐴𝐵 12 corresponding = =3 sides are 𝐸𝐹 4 𝐵𝐶 15 proportional = =3 𝐹𝐺 5 with a scale 𝐴𝐶 9 factor of 3. = =3 𝐸𝐺 3 ∆ABC is ~ ∆EFG Show you Know – Determine if each pair of triangles is similar. Assignment • Page 150 (4-7,9,10,12-14 PERIOD 1 BRING FOOD FOR THE MINGA FOOD BANK COLLECTION TOMORROW!!! 4.3 Similar Triangles Learning Outcome: To be able to solve problems involving similar triangles and find missing side lengths Use Similar Triangles to Determine a Missing Side Length Example 2: Kyle is drawing triangles for a math puzzle. Use your knowledge of similar triangles to determine a) If the triangles are L similar b) the missing side length K 21 T M 10.5 U 7 8 V Example 2 a) If the triangles are similar 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° L Compare corresponding Angles: K Note: It is not necessary to prove both conditions for similarity. One is sufficient. T M 1 U All pairs of corresponding angles are equal. Therefore, ΔKLM ~ ΔTUV 7 8 V Example 2 b) the missing side length You can compare corresponding sides to determine the scale K factor. 3 L The scale factor is 3. You can solve for the unknown length. T M 1 U 7 8 V Example 2 b) the missing side length Method 1: Use a scale factor K 3 x=31.5 L The missing side length is 31.5 units. T M 1 U 7 8 V Example 2 b) the missing side length Method 1: Use a Proportion Since the triangles are similar, you can use equal K ratios to set up a proportion. x1.5 L T M 1 x1.5 7 x=31.5 The missing side length is 31.5 units. U 8 V 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. Show you Know – Solve using a method of your choice Assignment • Page 150 (9-14) • Due Tuesday, October 23rd Assignment • Page 150 (1-2, 5, 7-9, 13-14) • Due Friday, October 18th