Proving Triangles Congruent

1
Lesson 5-3
Proving Triangles Similar
(AA, SSS, SAS)
2
AA Similarity (Angle-Angle)
If 2 angles of one triangle are congruent to 2
angles of another triangle, then the triangles
are similar.
and
Given
Conclusion
3
SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2
triangles are proportional, then the triangles
are similar.
Given
Conclusion
4
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.
Given
Conclusion
5
Similarity is reflexive, symmetric, and
transitive.
Proving Triangles Similar
Steps for proving triangles similar
1. Mark the Given. 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.
6
Given DEGF Prove DEC FGC
Problem 1
Step 1 Mark the given and what it implies
Step 2 Mark the vertical angles
AA
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




Given
Alternate Interior lts
Alternate Interior lts
AA Similarity
7
Problem 2

Step 1 Mark the given and what it implies
SSS
Step 2 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




Given
1. IJ 3LN JK 3NP IK 3LP
Division Property
Substitution
SSS Similarity
8
Given ABCD is a rectangle. Prove
Problem 3
Statements Reasons

9
Problem 4

Step 1 Mark the given and what it implies
Step 2 Mark the reflexive angles
SAS
Step 3 Choose a method (AA,SSS,SAS)
Step 4 List the Parts in the order of the method
with reasons Next Slide.
Step 5 Is there more?
10
Statements Reasons
G is the Midpoint of H is the Midpoint of Given
2. EG DG and EH HF Def. of Midpoint
3. ED EG GD and EF EH HF Segment Addition Post.
4. ED 2 EG and EF 2 EH Substitution
Division Property
Substitution
Reflexive Property
SAS Postulate