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How to Show Two Triangles are Similar

Test one simply states that if two triangles are similar they must be an equiangular. Both these triangles have the same shape but one is bigger than the other. However, they both have the same sized angles. So, we say they are equiangular. That means that these two triangles are classed as similar. Let’s look at an example to clarify this a little further. In this question we have to state why the following pair of triangles is similar. If we look at the triangles, each has two angles given and they aren’t the same.

Let’s start by finding the third angle in each, which might show that they’re equiangular. In triangle ABC, 67 plus 50 equals 117 degrees. Subtracting this from 180 degrees gives a third angle of 63 degrees. That means the both triangles have the same angles. Because triangle DEF also has angles of 63 and 67 degrees shown. So, the third angle must also be the same. Let’s write these equivalents down to show similarity. Angle BCA equals angle DFE. Angle ABC equals angle FDE. And therefore angle BAC equals angle FED. So, triangle ABC is similar to triangle FED. Reason: the triangles are an equiangular.

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