Similar Triangles and Ratios

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Presentation transcript:

Similar Triangles and Ratios MAP4C Similar Triangles and Ratios

Similar Triangles Triangles are similar if: a) they have the same angles, only the size of the triangle is larger b) the ratios of the side lengths are increased by the same factor (all increased by 3 times, or one-half) Use of symbols to represent the same angles like the degree symbol o, the arc symbol , any symbol like θ, α, Ф, β, ☺, ♥, ♦, ♪, etc.

Similar Triangles As two angles are the same, the third must also be as they both add up to 180 degrees.

Similar Triangles Example: Given the following triangles are similar, find the indicated unknown lengths: a 3 4 12 Set up a ratio: 12 = a 12(3) = 4a a = 36/4 = 9 4 3

Shadow Problem 14.4 m h 1.8 m 1.0 m A ratio exists: 14.4/1.8 = h/1 A metre stick casts a shadow 1.8 m long, and at the same time, a pole casts a shadow 14.4 m long. What is the height of the pole? 14.4 m h 1.8 m 1.0 m A ratio exists: 14.4/1.8 = h/1 h = 8 m

Solving Use primary trig ratios (SOH CAH TOA) Use Pythagorean Theorem, if needed. Draw a diagram if one is not provided. Set up a ratio that’s easy to solve (the unknown on the numerator). Complete Similar Triangle Worksheet