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.

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.