1. Aim: How to prove triangles are congruent using a 3rd shortcut: ASA.
Do Now:
Given:
T is the midpoint of PQ, PQ bisects RS, and RQ  SP. Explain how RTQ  STP.

2. RTQ  STP because of SSS  SSS
Do Now
You are given:
T is the midpoint of PQ, PQ bisects RS, and RQ  SP. Explain how RTQ  STP.
RQ  SP – we’re told so
(S  S)
PT  TQ – a midpoint of a segment cuts the segment into two congruent parts
(S  S)
RT  TS – a bisector divides a segment into 2 congruent parts
(S  S)
RTQ  STP because of SSS  SSS

3. Copied 2 angles and included side:
Sketch 14 – Shortcut #3 A B C
ABC  A’B’C’ 
Copied 2 angles and included side:
BC  B’C’, B  B’, C  C’ B’ A‘ C’
Measurements showed:
Shortcut for proving congruence in triangles:
ASA  ASA

4. If A =  A', AB = A'B',  B =  B', then DABC = DA'B'C'
Angle-Side-Angle
III ASA = ASA
Two triangles are congruent if two angles and the included side of one triangle are equal in measure to two angles and the included side of the other triangle. A A’ B C B’ C’
If A =  A', AB = A'B',  B =  B', then DABC = DA'B'C'
If ASA  ASA ,
then the triangles are congruent

5. Model Problems
Is the given information sufficient to prove congruent triangles?
YES
YES NO

6. Model Problems
Name the pair of corresponding sides that would have to be proved congruent in order to prove that the triangles are congruent by ASA.
DCA  CAB
DFA  BFC
DB  DB

7. ACE  BDE because of ASA  ASA
Model Problem
CD and AB are straight lines which intersect at E. BA bisects CD. AC  CD, BD  CD.
Explain how ACE  BDE using ASA
C  D –  lines form right angles and all right angles are  & equal 90o
(A  A)
CE  ED – bisector cuts segment into 2  parts
(S  S)
CEA  BED – intersecting straight lines form vertical angles which are opposite and 
(A  A)
ACE  BDE because of ASA  ASA

8. AED  BCD because of ASA  ASA
Model Problem
1  2, D is midpoint of EC, 3  4.
Explain how AED  BCD using ASA
1  2 – Given: we’re told so
(A  A)
ED  DC – a midpoint of a segment cuts the segment into two congruent parts
(S  S)
3  4 – Given: we’re told so
(A  A)
AED  BCD because of ASA  ASA

9. DEF  ABC because of ASA  ASA
Model Problem
DA is a straight line, E  B, ED  AB, FD  DE, CA  AB
Explain how DEF  ABC using ASA
E  B – Given: we’re told so
(A  A)
ED  AB – Given: we’re told so
(S  S)
EDF  BAC -  lines form right angles and all right angles are  & equal 90o
(A  A)
DEF  ABC because of ASA  ASA