Similar Triangles

What are similar triangles?

Answer: Similar triangles have the same 'shape' but are just scaled differently. Similar triangles have congruent angles and proportional sides. 
 

What is true about the angles of similar triangles?

Answer: They are congruent. as the picture below demonstrates.

What is true about the sides of similar triangles?

Answer: Corresponding sides of similar triangles are proportional. The example below shows two triangle's with their proportional sides ..

What is the similarity ratio (aka scale factor)?

Answer: It's the ratio between corresponding sides. In the picture above, the larger triangle's sides are two times the smaller triangles sides so the scale factor is 2

16⋅2 = 32

22⋅2 = 44

25⋅2 = 50

Notation: △ABC~△XYZ means that "△ABC is similar to △XYZ

How do you find the similarity ratio?

Answer: Match up any pair of corresponding sides and set up a ratio. Example

If △ABC~ △WXY, then what is the similarity ratio?

Step 1) Pick a pair of corresponding sides (follow the letters)

         AB and WX are corresponding.

           Follow the letters: △ABC ~ △WXY

Step 2) Substitute side lengths into proportion

           AB / WX = 7 / 21

Step 3) Simplify (if necessary)

          7 / 21 = 1 /3

Problem 1) Use your knowledge of similar triangles to find the side lengths below.