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

2. EXAMPLE 1
Use the AA Similarity Postulate
SOLUTION
Because they are both right angles, D and G are congruent.
By the Triangle Sum Theorem, 26° + 90° + m E = 180°, so m E = 64°. Therefore, E and H are congruent.
ANSWER
So, ∆CDE ~ ∆KGH by the AA Similarity Postulate.

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

4. EXAMPLE 2
Show that triangles are similar
SOLUTION a.
You may find it helpful to redraw the triangles separately.
Because m ABE and m C both equal 52°, ABE C. By the Reflexive Property, A A.
So, ∆ ABE ~ ∆ ACD by the AA Similarity Postulate.
ANSWER

5. EXAMPLE 2
Show that triangles are similar
SOLUTION b.
You know SVR UVT by the Vertical Angles Congruence Theorem. The diagram shows RS ||UT so S U by the Alternate Interior Angles Theorem.
So, ∆SVR ~ ∆UVT by the AA Similarity Postulate.
ANSWER

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

7. GUIDED PRACTICE
for Examples 1 and 2
Show that the triangles are similar. Write a similarity statement. 2.
∆ CDF and ∆ DEF
SOLUTION
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.

8. GUIDED PRACTICE
for Examples 1 and 2 3.
Reasoning
Suppose in Example 2, part (b), SR TU . Could the triangles still be similar? Explain.
SOLUTION
Yes; if S T, the triangles are similar by the AA Similarity Postulate.