Lesson 4.4

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Transcript 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. 𝐷𝐸 ≅ 𝐷𝐸
3. ∠𝐷𝐸𝐺 𝑎𝑛𝑑 ∠𝐷𝐸𝐹 are right
angles
4. ∠𝐷𝐸𝐺 ≅ ∠𝐷𝐸𝐹
5. ∆𝐷𝐸𝐹 ≅ ∆𝐷𝐸𝐺
6. EF ≌ EG
Reasons
1. Given
2. Reflexive Property
3. Given
4. All right angles are congruent
5. ASA
6.CPCTC
AAS
SAS
SSS
∆𝐴𝐵𝐶 ≅ ∆𝐸𝐵𝐷
∆𝐽𝐾𝐿 ≅ ∆𝑁𝑂𝑀
∆𝐺𝐻𝑈 ≅ ∆𝐺𝐵𝑈
AC ≅ ED
JK ≅ NO
∠H ≅ ∠B
CB ≅ DB
∠K ≅ ∠O
∠HUG ≅ ∠BUG
∠A ≅ ∠E
∠J ≅ ∠N
∠HGU ≅ ∠BGU
PROOFS WITH CPCTC
Reasons
Statements
1. ∠𝑄 ≅ ∠𝑅 and ∠𝑄𝑃𝑆 ≅
∠𝑅𝑆𝑃
2. PS ≅ SP
3. ∆𝑃𝑅𝑆 ≅ 𝑆𝑄𝑃
4. SQ ≅ PR
1. Given
2. Reflexive Property
3. AAS
4. CPCTC
Reasons
Statements
1. 𝑙 ⊥ 𝐴𝐵, 𝑙 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 𝐴𝐵 𝑎𝑡 𝐶,
and 𝑃 𝑖𝑠 𝑜𝑛 𝑙
2. ∠𝐴𝐶𝑃 𝑎𝑛𝑑 ∠𝐵𝐶𝑃 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡
𝑎𝑛𝑔𝑙𝑒𝑠
3. ∠𝐴𝐶𝑃 ≅ ∠𝐵𝐶𝑃
4. AC ≅ BC
5. 𝑃𝐶 ≅ 𝑃𝐶
6. ∆𝐴𝐶𝑃 ≅ ∆𝐵𝐶𝑃
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