6.5

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6.5 Prove Triangles Similar by SSS and SAS

• Geometry
• Ms. Rinaldi

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Side-Side-Side (SSS) Similarity Theorem

• If the corresponding side lengths of two
  triangles are proportional, then the triangles
  are similar.

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EXAMPLE 1
Use the SSS Similarity Theorem
SOLUTION
Remaining sides
Shortest sides
Longest sides
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EXAMPLE 1
Use the SSS Similarity Theorem (continued)
Remaining sides
Longest sides
Shortest sides
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Use the SSS Similarity Theorem
EXAMPLE 2
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EXAMPLE 3
Use the SSS Similarity Theorem
SOLUTION
Write proportion.
Cross Products Property
72 12x 12
Simplify.
7 x
Solve for x.
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EXAMPLE 3
Use the SSS Similarity Theorem (continued)
DF 3(x 1) 24
BC x 1 6
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Use the SSS Similarity Theorem
EXAMPLE 4
Find the value of x that makes
Q
Y
20
30
x 6
21
X
Z
12
P
R
3(x 2)
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Side-Angle-Side (SAS) Similarity Theorem

• If an angle of one triangle is congruent to an
  angle of a second triangle and the lengths of the
  sides including these angles are proportional,
  then the triangles are similar.

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EXAMPLE 5
Use the SAS Similarity Theorem
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EXAMPLE 5
Use the SAS Similarity Theorem (continued)
SOLUTION
Shorter sides
Longer sides
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EXAMPLE 6
Choose a method
Tell what method you would use to show that the
triangles are similar.
SOLUTION
Find the ratios of the lengths of the
corresponding sides.
Shorter sides
Longer sides
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Choose a method
EXAMPLE 7