# Triangle Congruency Proofs

### New York State Common Core Math Geometry, Module 1, Lesson 26 & Lesson 27

Student Outcomes

• Students complete proofs requiring a synthesis of the skills learned in the last four lessons.

Triangle Congruency Proofs

Classwork

Exercises for Lesson 26

1. Given: π΄π΅ β₯ π΅πΆ, π΅πΆ β₯ π·πΆ
π·π΅ bisects β π΄π΅πΆ, π΄πΆ bisects β π·πΆπ΅
πΈπ΅ = πΈπΆ
Prove: β³ π΅πΈπ΄ β β³ πΆπΈπ·

2. Given: π΅πΉ β₯ π΄πΆ, πΆπΈ β₯ π΄π΅
π΄πΈ = π΄πΉ
Prove: β³ π΄πΆπΈ ββ³ π΄π΅πΉ

3. Given: ππ½ = ππΎ, ππ = ππ, πβ πππ½ = πβ πππΎ
Prove: π½π = πΎπ

4. Given: π½πΎ = π½πΏ, π½πΎ β₯ ππ
Prove: ππ = ππΏ

5. Given: β 1 β β 2, β 3 β β 4
Prove: π΄πΆ β π΅π·

6. Given: πβ 1 = πβ 2, πβ 3 = πβ 4, π΄π΅ = π΄πΆ
Prove: (a) β³ π¨π©π« β β³ π¨πͺπ«
(b) πβ π = πβ 6

Exercises for Lesson 27

1. Given: π΄π΅ = π΄πΆ, ππ΅ = ππΆ
Prove: ππ΅ = ππΆ

2. Given: Square π΄π΅πΆπ β Square πΈπΉπΊπ,
ππ΄π΅, ππΈπΉ
Prove: β³ π΄ππ β β³ πΈππ

3. Given: π½πΎ = π½πΏ,π½π = π½π
Prove: πΎπ = πΏπ

4. Given: π΄π· β₯ π·π, π΄π΅ β₯ π΅π,
π΄π· β π΄π΅
Prove: β π·πΆπ β β π΅πΆπ

5. Given: π΄π = π΄π, π΅π = πΆπ,
ππ β₯ π΄π΅, ππ β₯ π΄πΆ
Prove: π΅π = πΆπ

6. Given: π΄π = π΅π, πβ π΄ππ΅ = πβ π΄ππ = 90Β°
Prove: ππ = ππ

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