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SECONDARY MATH 2
LESSON
CORE STANDARDS
II.5.G.SRT.4
II.5.G.SRT.5
5-2
OBJECTIVE
1. SWBAT apply properties of similar triangles to solve problems.
Definition of Similar Triangles
NOTES
ABC ~ XYZ
A
If two triangles are similar, then corresponding angles
are congruent and corresponding sides are proportional.
X
C
B
A  X, B  Y, C  Z
Z
Y
Proving
Similarity
Angle-Angle Similarity Postulate
If two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar.
Side-Side-Side Similarity Theorem
If the three sides of one triangle are proportional to the three corresponding sides in another triangle, then the
triangles are similar.
Triangle Proportionality Theorem
If a line intersects 2 sides of a triangle and is parallel to the third side,
then the two intersected sides are divided proportionally.
(converse is also true.)
C
A
D
E
B
EXAMPLES
1.
If ABC ~ XYZ, find the measure
of every missing side or angle.
2.
If ABC ~ XYZ, solve for x.
C
x+5
X
12
B
3.
2x – 2
Z
18
x+7
Y
Y
4.
Solve for x.
x+9
B
x–9
x+6
E
x – 11
C
X
B
Given AB CD , prove ABE DCE
Statements
Reasons
A
Z
x+2
15
8
59
C
A
85
A
D
PRACTICE 5-2
NAME______________________________
[SHOW YOUR WORK]
Solve for x.
1. ABC ~ XYZ
2.
x
5
X
C
12
x – 10
A
x
35
x–7
15
B
Z
Y
3.
ABC ~ XYZ
4.
2x
X
x–1
3x – 15
A
B
3x + 11
2x + 8
Y
2x – 13
C
4x + 3
x+1
Z
Complete the proof.
5. Given AB CD and AC ED
Prove that ABC DCE
A
B
Statements
Reasons
E
C
D
6. One triangle has side lengths in centimeters of 3, 7 and 8. Another triangle has side lengths in centimeters of 20,
7.5 and 17.5. Are the triangles similar? Show work to justify your answer.
7. Given that TUV RQP , and mT  42 , and T  Q , then what is the measure of  V ?
8. Given that a = b; Prove that LNM
Q
N
f
a
c
e
d
L
b
M
LMQ
Statements
Reasons