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Warm-Up Exercises
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
2. Solve
3.
They are the same.
x
= 54 .
9
18
ABC ~
ANSWER
DEF. Find x.
10
ANSWER
108
Warm-Up Exercises
Target
Show that triangles are similar.
You will…
Use the AA Similarity Postulate.
.
Vocabulary
Warm-Up Exercises
•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
EXAMPLE
Warm-Up1Exercises
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.
ANSWER
Similarity statement
So, ∆CDE ~ ∆KGH by the AA Similarity Postulate.
EXAMPLE
Warm-Up2Exercises
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
So, ∆ ABE ~ ∆ ACD by the AA Similarity Postulate.
A.
EXAMPLE
Warm-Up2Exercises
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
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Show that the triangles are similar. Write a similarity
statement.
1.
∆FGH and ∆RQS
ANSWER
In each triangle all three angles measure 60°, so by
the AA similarity postulate, the triangles are similar;
∆FGH ~ ∆QRS.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Show that the triangles are similar. Write a similarity
statement.
2.
∆CDF and ∆DEF
ANSWER
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.
EXAMPLE
Warm-Up3Exercises
Standardized Test Practice
SOLUTION
x ft = 50 ft
40 in.
64 in.
40x = 64(50)
x = 80
The flagpole is 80 feet tall.
The correct answer is C.
------64 in.
Warm-Up
Exercises
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?
ANSWER
36.25 in.
58 in.
5.
------64 in.
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 tree shadow
length of your shadow