Chapter 8 Lesson 3

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Chapter 8 Lesson 3

• Objective To use AA, SAS and SSS similarity
  statements.

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Postulate 8-1   Angle-Angle Similarity (AA )
Postulate                                       
                                             If
two angles of one triangle are congruent to two
angles of another triangle, then the triangles
are similar. ?TRS ?PLM
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Example 1 Using the AA Postulate
Explain why the triangles are similar. Write a
similarity statement.                    
                                                  
                           
RSW        VSB because vertical angles
are congruent.  R     V because their
measures are equal. ?RSW ?VSB by the
Angle-Angle Similarity Postulate.
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Example 2 Using the AA Postulate
Explain why the triangles are similar. Write a
similarity statement.                    
                                                  
                           
?AMX?BKX by AA Postulate
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Theorem 8-1   Side-Angle-Side Similarity (SAS )
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.
Theorem 8-2   Side-Side-Side Similarity (SSS )
Theorem If the corresponding sides of two
triangles are proportional, then the triangles
are similar.
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Example 3 Using Similarity Theorems
                                                
                                    Explain why
the triangles must be similar. Write a
similarity statement.
QRP     XYZ because they are right
angles. Therefore, ?QRP ?XYZ by the SAS
Theorem
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Example 4 Using Similarity Theorems
Explain why the triangles must be similar. Write
a similarity statement.                 
?ABC ?EFG by SSS Theorem
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Assignment
Pg. 435 1-9, 22, 24-27