### Lesson 4.4

```4-4 Using
Congruent
Triangles- CPCTC
*With SSS, SAS, ASA, and AAS, we know
how to use three parts of triangles to show
that the triangles are congruent. Once we
have triangles congruent, we can make
conclusions about the other parts because
by definition, corresponding parts of
congruent triangles are congruent.
EXAMPLE 1 (DO NOT COPY, JUST LISTEN)
EXAMPLE 2
Given: ∠DEG and ∠DEF are right
angles, and ∠EDG ≌ ∠EDF
Prove: EF ≌ EG
Statements
1. ∠EDG ≌ ∠EDF
2.  ≅
3. ∠  ∠ are right
angles
4. ∠ ≅ ∠
5. ∆ ≅ ∆
6. EF ≌ EG
Reasons
1. Given
2. Reflexive Property
3. Given
4. All right angles are congruent
5. ASA
6.CPCTC
AAS
SAS
SSS
∆ ≅ ∆
∆ ≅ ∆
∆ ≅ ∆
AC ≅ ED
JK ≅ NO
∠H ≅ ∠B
CB ≅ DB
∠K ≅ ∠O
∠HUG ≅ ∠BUG
∠A ≅ ∠E
∠J ≅ ∠N
∠HGU ≅ ∠BGU
PROOFS WITH CPCTC
Reasons
Statements
1. ∠ ≅ ∠ and ∠ ≅
∠
2. PS ≅ SP
3. ∆ ≅
4. SQ ≅ PR
1. Given
2. Reflexive Property
3. AAS
4. CPCTC
Reasons
Statements
1.  ⊥ ,     ,
and
2. ∠  ∠  ℎ

3. ∠ ≅ ∠
4. AC ≅ BC
5.  ≅
6. ∆ ≅ ∆
7. PA = PB
1. Given
2. Def. of ⊥
3. All right angles are congruent
4. Def. of Segment Bisector
5. Reflexive Property
6. SAS
7. CPCTC
HOMEWORK
Pg. 204 – 207 #’s 2-4, 6-12, 14, 23
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