Download Theorems about Parallel Lines

Proving Triangles are Congruent:
ASA and AAS
Sec 4.4
GOAL:
To prove triangles are congruent by
using the ASA Congruence Postulate
and the AAS Congruence Theorem
ASA Congruence Postulate

If two angles and the included side of one triangle are
congruent to two angles and the included side of a second
triangle, then the two triangles are congruent.
Included side – a side that is between two angles of a triangle
B
Q
P
A
C
If A  P and AB  PQ and B  Q,
then
ABC  PQR
R
AAS Congruence Theorem
If two angles and a nonincluded side of one triangle are congruent to
two angles and a nonincluded side of a second triangle, then the two
triangles are congruent.
Nonincluded side – a side that is not between two consecutive angles of a
triangle. Here, AC and PR are called nonincluded sides.

B
Q
P
A
C
If B  Q and C  R, and AC  PR,
then
ABC  PQR
R
Examples
Is
ABC  DEC ?
B
A
C
D
E
Examples
Is PQR  SRQ ?
Q
P
R
S
Examples
Is PQR  SRQ ?
P
R
Q
S
Two – Column Proof

Given: WZ bi sec ts XZY and XWY
Prove:
WZX  WZY
X
W
Z
Y
Example

Decide whether enough information is given to prove that
triangles are congruent. If yes, state the congruence postulate
you would use and the congruence statement.
P
Q
R
S
Example

Solve for x and y
(3 y  11)
55
(2 x)