Section 6.4 AA Similarity Review Triangle Angle Sum Theorem Three angles in a triangle have a sum of ______ Similar Figures Angles are _________, sides are ______________

So… if two angles of a triangle are 90° and 40°, what is the measure of the third angle? If two angles of another triangle are 90° and 40°, what is the measure of it’s third angle? What do you know about the two triangles?

They are SIMILAR triangles since all three angles are congruent. Do you always need to know the measure of the third angle to know if the triangles are similar?

Angle Angle (AA) Similarity Theorem If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. You can then write a similarity statement for the two triangles.

EXAMPLE 1 Use the AA Similarity Postulate Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

EXAMPLE 2 Show that triangles are similar Show that the two triangles are similar. a. ∆ABE and ∆ACD b. ∆SVR and ∆UVT

GUIDED PRACTICE for Examples 1 and 2 Show that the triangles are similar. Write a similarity statement. 1. ∆FGH and ∆RQS In each triangle all three angles measure 60°, so by the AA similarity postulate, the triangles are similar ∆FGH ~ ∆QRS. ANSWER

GUIDED PRACTICE for Examples 1 and 2 Show that the triangles are similar. Write a similarity statement. 2. ∆CDF and ∆DEF Since m CDF = 58° by the Triangle Sum Theorem and m DFE = 90° by the Linear Pair Postulate the two triangles are similar by the AA Similarity Postulate; ∆CDF ~ ∆DEF. ANSWER

EXAMPLE 3 Standardized Test Practice

GUIDED PRACTICE for Example 3 4. A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow? (The woman is 5 feet four inches tall and her shadow is 40 inches long.) ANSWER 36.25 in.

GUIDED PRACTICE for Example 3 5. You are standing in your backyard, and you measure the lengths of the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree. tree height your height = length of your shadow length of shadow SAMPLE ANSWER