Download Proving Triangles Similar

Lesson 6-3
Similar Triangles
The following must occur for triangles to be
similar, but there are other short cuts to prove
if triangles are similar (AA, SSS, SAS) :
1) The angles must be congruent
2) Sides must be proportional
Lesson 5-3: Proving Triangles
Similar
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AA Similarity (Angle-Angle)
If 2 angles of one triangle are congruent to 2 angles of
another triangle, then the triangles are similar.
E
B
A
C
Given:
D
F
and
Conclusion:
Lesson 5-3: Proving Triangles
Similar
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SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2 triangles
are proportional, then the triangles are similar.
E
B
5
A
10
8
11
C
D
16
22
F
Given:
Conclusion:
Lesson 5-3: Proving Triangles
Similar
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SAS Similarity (Side-Angle-Side)
If the measures of 2 sides of a triangle are proportional to the
measures of 2 corresponding sides of another triangle and the angles
between them are congruent, then the triangles are similar.
E
B
5
A
10
11
C
D
22
F
Given:
Conclusion:
Lesson 5-3: Proving Triangles
Similar
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Proving Triangles Similar
Similarity is reflexive, symmetric, and transitive.
Steps for proving triangles similar:
1. Mark the Given . . . and what it implies.
2. Mark … Shared Angles or Vertical Angles
3. Choose a Method. (AA, SSS , SAS)
Think about what you need for the chosen method and
be sure to include those parts in the proof.
Lesson 5-3: Proving Triangles
Similar
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Given : DE || FG
Problem #1
Pr ove : ▲ DEC
▲FGC
Step 1: Mark the given … and what it implies
Step 2: Mark the vertical angles
Step 3: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Step 5: Is there more?
Statements
Reasons
G
D
C
E
F
Lesson 5-3: Proving Triangles
Similar
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Problem
Given : IJ  3LN JK  3NP
#2 Pr ove : ▲ IJK ▲LNP
IK  3LP
Step 1: Mark the given … and what it implies
Step 2: Choose a method: (AA,SSS,SAS)
Step 4: List the Parts in the order of the method with reasons
Statements
Reasons
Step 5: Is there more?
J
K
N
I
IJ
JK
IK
2.
=3,
=3,
=3
LN
NP
LP
P
IJ
JK
IK
3.
=
=
LN NP LP
L
Lesson 5-3: Proving Triangles
Similar
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Given : G is the midpo int of ED
Problem #3
H is the midpo int of EF
Pr ove :
EGH
EDF
Step 1: Mark the given … and what it implies
Step 2: Mark the reflexive angles
Step 3: Choose a method: (AA,SSS,SAS)
E
G
H
D
Lesson 5-3: Proving Triangles
Similar
F
8
Determine whether each pair of
triangles is similar. Justify your
answer (AA, SSS, or SAS Similarity).
E
4.5
B
4
3
A
5
6
D
7.5
C
A
F
B
C
D
E
E
A
12
B
6
A
D
8
C
16
F
20
B
18
36
Lesson 5-3: Proving Triangles
Similar
C
24
9
Identify the similar triangles, and
find x and the measure of the
indicated sides.
AB and BC
A
x+3
B
E
5
3
2x - 8
D
C
Lesson 5-3: Proving Triangles
Similar
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Identify the similar triangles, and
find x and the measure of the
indicated sides.
A
AB and AC
x+2
8
E
5
D
B
6
C
Lesson 5-3: Proving Triangles
Similar
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If PR || KL, KN = 9, LN = 16, PM = 2(KP),
find KP, KM, MR, ML, MN, and PR.
L
N
R
Q
K
P
M
Lesson 5-3: Proving Triangles
Similar
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