?K ? ?N; segment KL ? segment NL ,triangle KLM is an isosceles triangle with base segment ML and triangle NLM is an isosceles triangle with base segment ML

Question

GIVEN: ∠K ≅ ∠N; segment KL ≅ segment NL ,triangle KLM is an isosceles triangle with base segment ML and triangle NLM is an isosceles triangle with base segment ML  

 

 PROVE: segment ML bisects ∠KLN

 

Prove the proof above in two different ways in a two-column format.

Answer 1

Proof 1

1) segment KL ≅ segment NL. Given

2) segment KL ≅ segment KM. Given

3) segment NL ≅ segment NM. Given

4) segment KM ≅ segment NM. Transitive PoE

5) ML = ML Reflexive PoE

6) Δ LKM ≅ Δ LNM SSS rule

7) ∠KLM ≅ ∠NLM CPCTC

8) ML bisects ∠KLN Angle Bisector Property QED

Proof 2

1) segment KL ≅ segment NL. Given

2) segment KL ≅ segment KM. Given

3) segment NL ≅ segment NM. Given

4) segment KM ≅ segment NM. Transitive PoE

5) ∠K ≅ ∠N Given

6) Δ LKM ≅ Δ LNM SAS rule

7) ∠KLM ≅ ∠NLM CPCTC

8) ML bisects ∠KLN Angle Bisector Property QED