In this lesson we’ll look at how to prove triangles are similar to one another.

In math, the word “similarity” has a very specific meaning.

Outside of math, when we say two things are similar, we just mean that they’re generally like one another.

Which triangle similarity theorem states that two triangles are congruent if the corresponding sides of two triangles are in proportion?

But in math, to say two figures are similar means that they have exactly the same shape, but that they’re different sizes. Here are examples of similar squares, similar pentagons, and similar triangles:

Which triangle similarity theorem states that two triangles are congruent if the corresponding sides of two triangles are in proportion?

Example

Are the triangles similar? Which theorem proves that they’re similar and complete the similarity statement.

???\triangle ABC\sim \triangle???____

Which triangle similarity theorem states that two triangles are congruent if the corresponding sides of two triangles are in proportion?

In a pair of similar triangles, all three corresponding angle pairs are congruent and corresponding side pairs are proportional.

Example

Are the triangles similar? Which theorem proves that they’re similar and complete the similarity statement.

???\triangle WXY\sim \triangle???____

finding the theorem that proves the triangle similarity

We know from the figure that ???\angle W\cong\angle V=59^\circ???. We also have a pair of vertical angles at ???Y???, and remember that vertical angles are congruent to one another.

connected similar triangles

Putting all this together, we can see say that the triangles are similar by Angle Angle (AA). When we match up the corresponding parts, the similarity statement is ???\triangle WXY\sim \triangle VZY???.