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