Transformations and SymmetrySimilar Triangles

Similar Triangles

The concept of similarity is particularly powerful with triangles. We already know that the corresponding internal angles in similar polygons are equal.

For triangles, the opposite is also true: this means that if you have two triangles with the same three angle sizes, then the triangles must be similar.

And it gets even better! We know that the internal angles in a triangle always add up to °. This means that if we know two angles in a triangle, we can always work out the third one.

For similarity, this means that we also just need to check two angles to determine if triangles are similar. If two triangles have two angles of the same size, then the third angle must also be the same in both.

This result is sometimes called the AA Similarity Condition for triangles. (The two As stand for the two angles we compare.)