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. C 12 9 A B F E G 4 3 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. 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. The corresponding sides are proportional with a scale factor of 3. ∆ABC is ~ ∆EFG Compare Corresponding Sides 𝐴𝐵 𝐸𝐹 = 12 4 =3 𝐵𝐶 𝐹𝐺 = 15 5 =3 𝐴𝐶 𝐸𝐺 = 9 3 =3 Compare Corresponding Angles ∠𝐴=90° 𝑎𝑛𝑑 ∠𝐸=90° ∠𝐵=37° 𝑎𝑛𝑑∠𝐹=37° ∠𝐶=53° 𝑎𝑛𝑑∠𝐺=53°

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 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 U V 7 8 M 10.5

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

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

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

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

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