1. 1. In ABC and XZW, m A = m X and m B = m Z
1. In ABC and XZW, m A = m X and m B = m Z. What can you conclude about m C and m W?
ANSWER
They are the same.
2. Solve = x 18 54 9
ANSWER
108
ABC DEF. Find x. ~
ANSWER 10

2. Show that triangles are similar. Use the AA Similarity Postulate.
Target
Show that triangles are similar.
You will…
Use the AA Similarity Postulate. .

3. Vocabulary
AA Similarity Postulate 22 –
If two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar.
Similarity statement

4. EXAMPLE 1
Use the AA Similarity Postulate
Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.
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.
Similarity statement
ANSWER
So, ∆CDE ~ ∆KGH by the AA Similarity Postulate.

5. EXAMPLE 2
Show that triangles are similar
Show that the two triangles are similar. a.
∆ABE and ∆ACD
SOLUTION
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.

6. X X EXAMPLE 2 Show that triangles are similar
Show that the two triangles are similar. b.
∆SVR and ∆UVT X X
SOLUTION
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.
Are they similar if the sides are not parallel? No

7. 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

8. 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

9. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
SOLUTION
x ft
64 in.
50 ft
40 in. =
40x = 64(50)
x = 80
64 in.
The flagpole is 80 feet tall. The correct answer is C.

10. GUIDED PRACTICE for Example 3 4.
What If ? A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow?
58 in.
ANSWER
36.25 in.
64 in. 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 tree shadow