Transcript 7-3 Proving Triangles Similar AA SAS SSS

Objectives
• Prove that two triangles are similar using
AA, SAS, and SSS
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Proving Two Triangles Similar with Shortcuts
• Instead of using the definition of similarity
to prove that two triangles are congruent
(all corresponding angles are congruent
and all corresponding sides are
proportional), you can use three shortcuts:
– Angle-Angle (AA)
– Side-Angle-Side (SAS)
– Side-Side-Side (SSS)
2
Angle-Angle (AA) Similarity Postulate
• If two angles of one triangle are congruent
to two angles of another triangle, then the
triangles are similar.
3
AA Example
Explain why the triangles are similar and
write a similarity statement.
∠R ≅ ∠V (Given)
∠RSW ≅ ∠VSB (vertical angles are congruent)
ΔRSW ≅ ΔVSB (AA)
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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
sides including the two angles are
proportional, then the triangles are similar.
G
A
2
4
B
3
C
J
ΔABC ~ ΔGJH
6
H
5
SAS Example
Explain why the two
triangles are similar
and write a similarity
statement.
∠Q ≅ ∠X since they are
right angles
The two sides that
include the right
angles are
3 6

proportional
4
8
By SAS, ΔPRQ ~ΔZYX
6
Side-Side-Side (SSS) Similarity Theorem
• If the corresponding sides of two triangles
are proportional, then the triangles are
similar.
G
A
4
5
8
B
6
10
C
J
ΔABC ~ ΔGJH
12
H
7
SSS Example
Explain why the two triangles are similar and write
the similarity statement.
AC CB AB 3



EG GF EF 4
Since all sides of the two triangles are proportional,
by SSS, ΔABC ~ ΔEFG
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