Lesson on AA Similarity Property

​Before we start the lesson, let's review the shortcuts for determining when triangles are congruent. This concept will come in handy in today's lesson.

Multiple Choice

Which of the following is NOT a way to determine when two triangles are congruent?

• SSS

• SAS

• AAS

• SSA

Multiple Choice

Why are the triangles congruent?

• HL

• SAS

• SSS

• ASA

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS

• SAS

• ASA

• AAS

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS

• SAS

• ASA

• AAS

Multiple Choice

Are the triangles congruent, if yes, why?

• SSS

• SAS

• ASA

• Not Congruent

Multiple Choice

Now let's go back to the subject at hand- similarity!

How do you determine when two polygons are similar?

• If all pairs of sides are congruent, then the polygons are similar.

• If all pairs of angles are congruent, then the polygons are similar.

• If all pairs of sides are proportional then the polygons are similar.

• If all pairs of sides are proportional and all pairs of angles are congruent, then the polygons are similar.

To tell if two polygons are similar, you need to know that ALL pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

However...this is only if the figure has more than three sides. If the polygons are triangles, well...you don't need to know all of that pesky information to tell they are similar.

TRUTH

​To prove that two triangles are similar, you will use one of the following:
SSS Similarity Property

AA Similarity Property

and

SAS Similarity Property.

Please open up your notes.

​Copy this into your notes.

Multiple Choice

What is the sum of the angles in any triangle?

• 180

• 90

• 360

• 45

Use the fact that the sum of the angles in any triangle is 180 to find the missing angle measures in example 1. Write the measures in the triangles.

This is what you should have gotten.

Since you have two pairs of congruent angles, the triangles are similar. Copy the rest of the example.

Find the missing angle measures.

Since you have two pairs of congruent angles, the triangles are similar. Copy the rest of the example.

Since you only have one pair of congruent angles, the triangles are not similar.

For example 3, you have a pair of equal, vertical angles. Mark them as being congruent.

In this example, you have two 48 degree angles. But you also know that the measure of angle R is the same for both triangles. To show that it's the same in both triangles, simply put arcs at angle R. See the next screen.

Copy the rest of example 4.

Do you see that the smaller triangle and the larger triangle have TWO pairs of congruent angles? Therefore the triangles are similar.

Now it's your turn to use AA similarity property.

Multiple Choice

Find the missing angles. Are the triangles similar by the AA similarity property?

• Yes

• No

Multiple Choice

Are the triangles similar by the AA similarity property?

• Yes

• No

Multiple Choice

Are these two triangles similar by AA sim. property?

• Yes

• No

Multiple Choice

Are these two triangles similar by AA similarity property?

• Yes

• No

Multiple Choice

Are these triangles similar using the AA similarity property?

• yes

• no

Multiple Choice

Are these two triangles similar using the AA similarity property?

• Yes

• No

Multiple Choice

Which triangles are similar to triangle A? (HINT: Find the missing angle measures.)

• B

• C

• Both

• None