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4.4 Proving Triangles are Congruent: ASA and AAS
Learning Targets: I can use the ASA Postulate to prove that triangles are congruent.
I can use the AAS Postulate to prove that triangles are congruent.
ANGLE-SIDE-ANGLE (ASA) POSTULATE
If two angles and the ___________________ side of one triangle are congruent to two angles and
the ___________________ side of a second triangle, then the two triangles are _____________.
If
Angle  A   D
Side AC  DF
Angle  C   F
Then Δ______  Δ_______
B
A
E
C D
F
Ex 1) Given: BC  EC
B  E
Prove: ΔABC  ΔDEC
Statements
C
Statements
B
E
Reasons
X
Ex 2) Given: WZ bisects  XZY &  XWY
Prove: ΔZXW  ΔZYW
A
D
Z
Reasons
W
Y
ANGLE-ANGLE-SIDE (AAS) POSTULATE
If the two angles and a ___________________ side of one triangle are congruent to two angles and a
___________________ side of a second triangle, then the two triangles are __________________.
If
P  W
Angle
Angle
Side
Q
Q  X
X
QS  XY
S
P
Then Δ_______  Δ________
Ex 3) Given: BD  BC
AD EC
Prove: ΔABD  ΔEBC
W
A
Y
C
B
D
E
Reasons
Statements
Ex 4) Is it possible to prove the triangles congruent?
M
O
N
L
P
Ex 5) Can you draw two different triangles with all three angles congruent? (AAA)
Ex 6) Can you draw two different triangles with one pair of angle congruent and the two pairs of consecutive
sides congruent? (SSA)