Question

Determine the similarity of the triangle and similarity of polygon

Answer 1

Triangles, triangles, triangles! Why do they get all the attention?

It's so hard being the younger sibling of the strongest and most stable shape there is. How about some love for the rest of the shapes? Can't we talk about any of them being similar, too?

Well, sure. It turns out all circles are similar. So are all squares. And if a pentagon, hexagon, octagon, or any other n-gon is regular, then it's similar to all of its regular like-sided n-gons as well. Just like equilateral triangles.

Sample Problem

Determine if these two polygons are similar.



We are given that in pentagon A, the five sides and five angles are all congruent to each other, which makes it a regular pentagon. Same for pentagon B.

Since regular polygons with the same number of sides are always similar, we can determine that pentagon A is similar to pentagon B.

What about irregular shapes?



Two irregular shapes could be similar, but there's no quick rule about them, so we'll have to check that all of their corresponding side lengths are proportional and all of their corresponding angles are congruent.