Similar Triangles

 What is the similarity ratio? 

The similarity ratio is the proportion that you get when you divide any corresponding side of one triangle by its corresponding side in other similar triangle.

The Symbol for Similar: ~

These two triangles have a similarity ratio of ½ or of 2.
It depends on which triangle's sides you put in the numerator. As long as you remain consistent, your similarity ratio will hold true.

Since we know that the two triangles are similar, all that we have to do in order to find the simlarity ratio is to match a pair of corresponding sides! And then to divide!

Step 1) match a pair of corresponding sides
TU and TW are corresponding


Step 2) Divide the corresponding sides
TW ÷ TU = 40/10 = 4/1
Therefore, the similarity ratio is 4/1 from TWX to TUV

Alternately, you could have found the similarity ratio from the smaller triangle, TUV, to the larger TWX. TU÷ TW = 10/40 = 1/4

AB = 20

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AD = 30
What is the similarity ratio?
 The similarity ratio 
Similarity Ratio = 2/3 if we divide AB by AD

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AE = 33, how long is AC?

 Side AC's Length  

AC = 33 × 2/3 = 22

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ED = 27, how long is CB?

 Side CB's Length  
CB = 27 × 2/3 = 18

 How to find the similarity ratio  

TUV ~ TWX

TU = 10 and TW = 40, what is the similarity ratio?


 Show Ratio  
To find the similarity ratio, just divide a pair of corresponding sides.

TW ÷ TU = 40/10 = 4.
Remember that you can always go in the opposite direction, and do TU ÷ TW = 10/40 = ¼.