Triangle Similarity Using ASA and AAS

1. 5-6
ASA & AAS

2. Proving Triangles
Congruent
jc-schools.net/PPT/geometrycongruence.ppt

3. Angle-Side-Angle (ASA)
Congruence Postulate
Two angles and the INCLUDED side

4. Angle-Side-Angle (ASA)
Postulate 8-3:
If two angles and the included side of
one triangle are congruent to two angles
and the included side of another triangle,
then the two triangles are congruent.

5. Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
3.  B   E
ABC   DEF
included
side
jc-schools.net/PPT/geometrycongruence.ppt

6. Before we start…let’s get a few things straight
C
A B
Y
X Z
INCLUDED SIDE

7. Included Side
The side between two angles
GI HI GH

8. Included Side
Name the included side:
Y and E
E and S
S and Y
E
Y S
YE
ES
SY

9. Angle-Angle-Side (AAS)
Congruence Postulate
Two Angles and One Side that is
NOT included

10. Angle-Angle-Side (AAS)
Theorem 8-1:
If two angles and the nonincluded
side of one triangle are congruent to two
angles and the nonincluded side of
another triangle, then the two triangles
are congruent.

11. Angle-Angle-Side (AAS)
1. A  D
2.  B  E
3. BC  EF
ABC   DEF
Non-included
side
jc-schools.net/PPT/geometrycongruence.ppt

12. Warning: No SSA Postulate
B
There is no such
thing as an SSA
postulate!
A C
E
D
F
NOT CONGRUENT
jc-schools.net/PPT/geometrycongruence.ppt

13. Warning: No AAA Postulate
B
A C
E
D
F
There is no such
thing as an AAA
postulate!
NOT CONGRUENT
jc-schools.net/PPT/geometrycongruence.ppt

14. }Your Only Ways
To Prove
Triangles Are
Congruent

15. Name That Postulate
(when possible)
ASA
AAA
SSA
jc-schools.net/PPT/geometrycongruence.ppt

16. Things you can mark on a triangle when they aren’t
marked.
Overlapping sides are
congruent in each
triangle by the
REFLEXIVE property
Vertical
Angles are
congruent
Alt Int
Angles are
congruent
given
parallel lines

17. Ex 1
ΔDEF ΔLMN D N DE NL
In and , , and
E L
. Write a congruence statement.
  
   
 D E F   N L M

18. Ex 2
What other pair of angles needs to be
marked so that the two triangles are
congruent by AAS?
F
D
E
M
L
N
E N

19. Ex 3
What other pair of angles needs to be
marked so that the two triangles are
congruent by ASA?
F
D
E
M
L
N
DL

20. Determine if whether each pair of triangles is congruent by
ASA or AAS. If it is not possible to prove that they are
congruent, write not possible.
ΔGIH  ΔJIK by
AAS
G
I
H J
K
Ex 4

21. Determine if whether each pair of triangles is congruent by
ASA or AAS. If it is not possible to prove that they are
congruent, write not possible.
B A
ΔABC  ΔEDC by
ASA
C
D E
Ex 5

22. Determine if whether each pair of triangles is congruent by
ASA or AAS. If it is not possible to prove that they are
congruent, write not possible.
J K
M L
ΔJMK  ΔLKM by SAS or
ASA
Ex 7

23. Determine if whether each pair of triangles is congruent by
ASA or AAS. If it is not possible to prove that they are
congruent, write not possible.
Not possible
K
J
L
T
U
Ex 8
V