4.3: Triangle Congruence by ASA and AAS
4.4: CPCTC
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-Ace Ventura
Congruent Triangles
Postulate 4-3: Angle-Side-Angle (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.
HGB  NKP

Proving Triangles Congruent
Given : M  P
N is the midpoint of MP
Prove : NML  NPO
Statements
1.
M  P
N is the midpoint of MP
Reasons
1.
2. MN  PN
2.
3. MNL  PNO
3.
4. NML  NPO
4.
Congruent Triangles
Theorem 4-2: Angle-Angle-Side (AAS) Theorem: If two angles
and a nonincluded side of one triangle are congruent to two angles
and the corresponding nonincluded side of another triangle, then
the triangles are congruent.
CDM  XGT

Proving Triangles Congruent
Given : XQ || TR, XR bisects QT
Prove : XMQ  RMT
Statements
1. XQ || TR,
XR bisects QT
Reasons
1.
2.
2. Alternate Interior Angles Theorem
3. QM  TM
3.
4. XMQ  RMT
4.
Proving Triangles Congruent
X
Given : XZ bisects WXY
XZ  WY
Prove : WXZ  YXZ
Statements
1 2
W
Z
Reasons
1. XZ bisects WXY
1.
2. WXZ  YXZ
2.
3. 1 and 2 are right angles
3.
4. 1  2
4.
5. XZ  XZ
5.
6. WXZ  YXZ
6.
XZ  WY
Y
Section 4.4: Using Congruent Triangles
CPCTC: Corresponding Parts of Congruent
Triangles are Congruent.
Once two triangles have been proven congruent
this is used to make conclusions about the other
parts of the triangles.
Proving Triangles Congruent
Given : QPS  RSP , Q  R
Prove : SQ  PR
Statements
1. QPS  RSP ,
Reasons
Q  R
1.
2.
2.
3. QPS  RSP
3.
4. SQ  PR
4.
Reflexive Property
Proving Triangles Congruent
Statements
1.YX
 YZ , XYW  ZYW
Reasons
1.
2.
2.
3. XYW  ZYW
3.
4. XW  ZW
4.
Reflexive Property
4.3: Triangle
Congruence
by ASA and
AAS
4.4: CPCTC
Homework 4.3:
#1,2,5,6,11-14
Homework 4.4:
#2,8,14
“I wish, for just one day, Dad couldn't tell a lie.“
“I wish, for just one day, Dad couldn't tell a lie.“
-Max