1. Similar Triangles and Ratios
MAP4C
Similar Triangles and Ratios

2. 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.

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

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

5. 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

6. 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