AA Similarity Postulate
Easily Explained w/ 11 Step-by-Step Examples!

In today’s geometry lesson, you’re going to learn all about the AA similarity postulate.

This postulate is the 1st of 3 postulates we’re going to review. The other two include SSS (side-side-side) and SAS (side-angle-side) which we’ll cover in the next lesson.

So let’s jump in!

Did you know that the shape of a triangle is entirely determined by the measure of its angles?

That means, if we can prove two triangles have three congruent angles, then the triangles are similar.

But here’s the cool part…

…we only need to prove two angles of one triangle are congruent to two angles of another triangle to show similar triangles.

Why?

Because if we know two angles, we can find the third using the triangle sum theorem (i.e., all interior angles of a triangle sum to 180 degrees). Therefore, if we know two angles are equal, all three angles must be equal, as Math is Fun accurately states.

And if we know that if two triangles are similar, then their corresponding sides are proportional.

Which means, all we have to do is find our scale factor, and we can solve for missing side lengths.

Therefore, we are going to use our AA Similarity Postulate to:

1. Determine if two triangles are similar.
2. Find indicated side lengths by using proportions.
3. Write some two-column proofs using our knowledge of similarity.

AA Postulate – Lesson & Examples (Video)

45 min

• Introduction AA Similarity for Triangles
• 00:00:27 – Overview of AA Similarity Postulate (Examples #1-4)
• Exclusive Content for Member’s Only

• 00:12:18 – Given AA similarity, find the altitude or indicated side length (Examples #5-7)
• 00:25:47 – Given AA similarity, solve for x and y (Examples #8-9)
• 00:37:34 – Write a two-column proof using the AA similarity postulate for triangles (Examples #10-11)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions