Objectives

1
Objectives

• Prove that two triangles are similar using AA,
  SAS, and SSS

2
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)

3
Angle-Angle (AA) Similarity Postulate

• If two angles of one triangle are congruent to
  two angles of another triangle, then the
  triangles are similar.

4
AA Example

• Explain why the triangles are similar and write a
  similarity statement.
• ?R ? ?V (Given)
• ?RSW ? ?VSB (vertical angles are congruent)
• ?RSW ? ?VSB (AA)

5
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
C
3
J
6
H
?ABC ?GJH
6
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
  proportional

By SAS, ?PRQ ?ZYX
7
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
10
B
C
6
J
12
H
?ABC ?GJH
8
SSS Example

• Explain why the two triangles are similar and
  write the similarity statement.
• Since all sides of the two triangles are
  proportional, by SSS, ?ABC ?EFG