Download 7-3: Identifying Similar Triangles

7-3: Identifying Similar
Triangles
Expectations:
G2.3.2: Use theorems about congruent
triangles to prove additional
theorems and solve problems.
G2.3.3: Prove that triangles are similar
by SSS, SAS and AA conditions for
similarity.
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7-3 Similar Triangles
Angle-Angle
a. Draw two triangles with angle
measures of 75° and 65°.
b. Label the 75° angles ∠A and ∠X.
c. Label the 65° angles ∠B and ∠Y.
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7-3 Similar Triangles
Angle-Angle
d. Compare the ratios of
corresponding sides.
e. What does this tell us about
the triangles?
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7-3 Similar Triangles
Angle-Angle Triangle
Similarity Theorem
If two angles of a first triangle are
congruent to two angles of a second
triangle, then the triangles are
similar.
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7-3 Similar Triangles
Side-Side-Side
a. Draw ∆ABC such that AB = 4,
BC = 6 and AC = 7.
b. Draw ∆DEF such that DE = 8,
EF = 12 and DF = 14.
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7-3 Similar Triangles
Side-Side-Side
c. Compare corresponding angles.
d. What is true about the triangles?
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7-3 Similar Triangles
Side-Side-Side Triangle
Similarity Theorem
If the measures of the corresponding
sides of 2 triangles are proportional,
then the triangles are similar.
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7-3 Similar Triangles
Side-Angle-Side
a. Draw ∆KLM such that KL = 4,
LM = 5 and m∠L = 60°.
b. Draw ∆RST such that RS = 8,
ST = 10 and m∠S = 60°.
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7-3 Similar Triangles
Side-Angle-Side
c. What is true about the
triangles?
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7-3 Similar Triangles
Sid-Angle-Side Triangle
Similarity Theorem
If the measures of two sides of one
triangle are proportional to two sides
of a second triangle and the included
angles are congruent, then the
triangles are similar.
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7-3 Similar Triangles
Equality Properties of
Similarity
Similarity of figures is reflexive,
symmetric and transitive.
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7-3 Similar Triangles
Reflexive Property of
Similarity
F~F
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7-3 Similar Triangles
Symmetric Property of
Similarity
If F ~ G, then G ~ F.
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7-3 Similar Triangles
Transitive Property of
Similarity
If F ~ G and G ~ H, then F ~ H.
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7-3 Similar Triangles
Are the following triangles
similar? Justify your response.
7.2
12
20
12
9
15
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Are the triangles below similar?
Justify with a postulate or theorem.
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7-3 Similar Triangles
If AB // EF, AD = 9, DB = 16, EC =
2(AE), determine AE, AC, BC and EF
C
H
E
A
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F
B
D
7-3 Similar Triangles
Use similar triangles to answer the
question below.
At 4:00 a yard stick cast a 5 foot shadow.
How tall is a tree that has an 18 foot
shadow at the same time?
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7-3 Similar Triangles
In the figure below, segment AB ⊥ segment DE. The
measure of ∠CAD is equal to the measure of
∠CEB. The length of segment CA is 6 units and
the length of segment CE is 187 units. If the
length of segment AD is 10 units, what is the
length of segment EB? B
A. 10
B. 20
D
C. 25
10
D. 30
C
6
E. 35
18
A
E
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Solve for x.
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7-3 Similar Triangles
Given: LP // MN
LJ
PJ
Prove:

LN JM
L
P
J
M
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N
7-3 Similar Triangles
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7-3 Similar Triangles
Assignment
pages 358 – 361,
# 13-23 (odds), 27, 37, 39-47 (all).
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7-3 Similar Triangles