1. Congruence Problems
Using the theorems

2. Congruency Thms. SSS ASA SAS RHS (or AAS)x
List the 4 triangle congruency thms.
Hypotenuse
SSS
ASA
(or AAS)
SAS
RHS

3. -Consider this- SAS Why are the two triangles congruent? D
What are the corresponding vertices?
What are the corresponding sides? A B C D E F
SAS
A   D
C   E
B   F

4. -Example 1- G
Draw a triangle GHI in which:
6 cm I
mG = 90°
mG= 90°,
30°
mH = 30°
mH = 30°. H
Will everyone else’s drawing be congruent to yours?
Why or why not?

5. -Example 2- SSS A reflection Why are the two triangles congruent?
Name the corresponding vertices
What isometry maps ADB onto CDB? A
SSS D B
A   C
ADB   CDB
ABD   CBD C
A reflection

6. -Example 3- S A S A Given: A is a midpoint of Prove: BAE   DAC.
A is midpoint of BD
BAE  DAC
Vert. opposite angles
A is midpoint of EC
 BAE  DAC
By SAS property

7. -Example 4- S S Given: Prove: B  D      ABC  CDA  B  D
Reflexive property
 ABC  CDA
By SSS property    
 B  D
Corresponding ’s in congruent ’s are congruent

8. -Example 5- R R H H S S Given: Prove:    mQSR = mPRS = 90°T
Given:
mQSR = mPRS = 90°
Prove:
QSR  PRS = 90° R H S R H S
Given
Given
Reflexive property
 QSR  PRS
By RHS property   
Corresponding sides in congruent ’s are congruent