Download ASA Postulate

Aim: How do we prove triangles congruent using
Angle-Side-Angle Postulate?
Do Now:
In each example, state whether or not the S.A.S. Postulate
can be used to prove the triangles congruent.
1)
2)

X
3)
4)
X
Geometry Lesson: A.S.A. Postulate
X
1
Postulate: Angle-Side-Angle Postulate (ASA):
Postulate:
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.
Complete
the an
triangle
by extending
the unfinished
Construct
identical
triangle using
sides.
triangles
willincluded
be congruent
twoThe
angles
and the
side.
Ex: Which sides or angles must be proved congruent in order
to prove the triangles congruent using the A.S.A Postulate?
C
A
B
B
2)
3)
1)
E
(
B
A
D
C
A
D
C
D
AC  AC 2
AED  BEC
A  C
(
Ex 1: Proof w/A.S.A.
Given: A  D
CB bi sec ts AD
Prove: ABX  DCX
A
1
2 X
C
D
Statement
1)
2)
3)
4)
5)
6)
A  D (a)
CB bi sec ts AD at X
X is midpoint of AD
AX  XD
(s)
1  2
(a)
ABX  DCX
B
Reason
1)
2)
3)
4)
5)
Given
Given
Def. line bisector
Def. midpoint
Vertical angles are
congruent.
6) A.S.A. Postulate
Geometry Lesson: A.S.A. Postulate
3
A
Ex 2,3,4: Proofs w/A.S.A.
2) Given: ADE  BDC, E  C
D is midpoint of EC
Prove: ADE  BDC
E
3) Given: AC bisects EB at D
AE  EB, CB  EB
Prove: AED  CBD
B
C
D
A
B
E
D
B
4) Given: BP  AC
BP bisects ABC
Prove: ABP  CBP
A
Geometry Lesson: A.S.A. Postulate
P
C
C
4
A
Ex 5,6: Proofs w/A.S.A.
5) Given: BCDE , ACB  FDE
B  E , BD  EC
B
Prove: CBA  DEF
C
D
Geometry Lesson: A.S.A. Postulate
E
D
A
6) Given: DB bisects ABC
DB bisects ADC
Prove: ABD  CBD
F
B
C
5