Triangle Similarity:

Angle Angle

Recall

• Recall the definitions of the following:• Similar• Congruent

• Also recall the properties of similarity we discussed yesterday• Corresponding angles in similar figures are congruent• The ratio of corresponding sides in a figure are equal

There’s another way

• There are other ways to prove figures are similar• Today we are looking at triangle similarity • Mainly involving the angle-angle similarity postulate

Angle-Angle similarity postulate• If two angles of one triangle are

congruent to two angles of another triangle, then the two triangles are similar

• This postulate allows you to say that two triangles are similar if you know that two pairs of angles are congruent.

• You don’t need to compare all of the side lengths and angle measures to show that two triangles are similar.

Third Angle Theorem

• If two angles in one triangle are congruent to two angles in another triangle, then the third angles must be congruent also.

Using the AA similarity postulate

• Determine whether the triangles are similar. If they are similar, write a similarity statement. Explain your reasoning.

Using the AA similarity postulate

• Are you given enough information to show that ∆RST is similar to ∆RUV? Explain your reasoning.

Determine whether the triangles are similar. If they are similar, write a similarity statement.

Using AA postulate to find the missing side