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TODAY IN GEOMETRY…
Review: Finding congruent angles and sides and proving triangles are congruent.
Learning Goal: 4.6 Use CPCTC to prove congruent parts of a triangle
Independent practice
AT – Proof-A-Rama 1 corrections
PRACTICE:
Find all 6 corresponding parts
△ 𝐵𝐴𝐶≅△𝐶𝐷𝐵𝐵
𝐶
𝐴
𝐷
Congruent Sides: Congruent Angles:
𝐴
𝐵𝐸𝐷
𝐶
PRACTICE: Which postulate would you use to state that the triangles are congruent. Then tell which triangles are congruent.
𝐷
𝐴
𝐵
𝐸
𝐶
△𝐵𝐴𝐷≅△ 𝐵𝐸𝐶
𝐴𝑆𝐴 𝑆𝑆𝑆△ 𝐵𝐴𝐸≅△𝐷𝐸 𝐴
ORDER MATTERS: When writing congruent triangles, make sure all angles and sides correspond!
CPCTC: Corresponding parts of congruent triangles are congruent.
EXAMPLE:Given that , the all parts (sides and angles) of the triangles are congruent:
𝐴 𝐶
𝐵
𝐹
𝐸𝐷
Congruent Sides: Congruent Angles:
Using CPCTC in proofs:
We use CPCTC to prove that parts of a triangle are congruent.
We MUST PROVE TRIANGLES ARE CONGRUENT FIRST!
1. USE one postulate to prove triangles are congruent.
2. What other information do I need?
3. What are the congruent triangles?
4. Use CPCTC
1. SSS
2.
3.
4.
1. AAS
2.
3.
4.
Given:
Prove:
STATEMENT REASON1. 1. Given
2. 2. Reflexive Property
3.
3. AAS
𝐴𝐴𝑆
4. 4. CPCTC
𝐴
𝑋 𝑌 𝑍
12
*we’re proving congruent sides!!!!-use CPCTC
Given:
Prove:
STATEMENT REASON1. 1. Given
2. 2. Definition of bisector
4.
4. SAS
𝑆
𝐴𝑆
5. 5. CPCTC
𝑊𝑋
𝑌
𝑍
3. 3. Reflexive Property
*we’re proving congruent sides!!!!-use CPCTC
HOMEWORK #7:
Pg. 259: 3-8, 10, 11, 21
If finished, work on other assignments:
HW #1: 221: 1-26, 32, 35-37HW #2: Pg. 228: 3-10, 15-16, 19-21 Pg. 231: 33-40HW #3: Pg. 236: 5, 7, 9-12, 24, 26 (Graph paper needed)HW #4: Pg. 243: 3-15, 20-22, 25-27, 35-37HW #5: Pg. 252: 3-5, 8-13, 18-20, 33, 34, 36-43HW #6: Proof-A-Rama 1