Geometry 5-6 ASA and AAS
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5-6 ASA & AAS
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Triangle Similarity Using ASA and AAS
Transcript of Geometry 5-6 ASA and AAS
5-6ASA & AAS
Proving Triangles Congruent
jc-schools.net/PPT/geometrycongruence.ppt
Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side
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.
Angle-Side-Angle (ASA)
1. A D2. AB DE
3. B E
ABC DEF
B
A
C
E
D
F
included side
jc-schools.net/PPT/geometrycongruence.ppt
Before we start…let’s get a few things straight
INCLUDED SIDE
A B
C
X Z
Y
The side between two angles
Included Side
GI HI GH
Name the included side:
Y and E
E and S
S and Y
Included Side
SY
E
YE
ES
SY
Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included
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.
Angle-Angle-Side (AAS)
1. A D
2. B E
3. BC EF
ABC DEF
B
A
C
E
D
F
Non-included side
jc-schools.net/PPT/geometrycongruence.ppt
Warning: No SSA Postulate
A C
B
D
E
F
NOT CONGRUENT
There is no such thing as an SSA
postulate!
jc-schools.net/PPT/geometrycongruence.ppt
Warning: No AAA Postulate
A C
B
D
E
F
There is no such thing as an AAA
postulate!
NOT CONGRUENTjc-schools.net/PPT/geometrycongruence.ppt
}Your Only Ways To Prove
Triangles Are Congruent
Name That Postulate(when possible)
ASAAAA
SSA
jc-schools.net/PPT/geometrycongruence.ppt
Overlapping sides are congruent in
each triangle by the REFLEXIVE property
Vertical Angles
are congruen
t
Alt Int Angles are congruent
given parallel
lines
Things you can mark on a triangle when they aren’t marked.
Ex 1
statement. congruence a Write.
and ,, and In
LE
NLDENDΔLMNΔDEF
DEF NLM
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
NE
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
LD
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
KEx 4
ΔABC ΔEDC by ASA
B A
C
ED
Ex 5
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.
ΔJMK ΔLKM by SAS or ASA
J K
LM
Ex 7
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
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.
V
