Question

Write a two column proof. Given and bisects KLM and MJK. Prove LKJ ~ LMJ

Answer 1

Answer:

ΔLKJ = ΔLMJ

Step-by-step explanation:

Statement Reasons

LJ = angle bisector of ∠KLM and ∠MJK Given

∠JLK ≅ ∠JLM   Definition of angle bisector    

∠KJL ≅ ∠MJL  Definition of angle bisector    

LJ ≅ LJ   LJ is a common side to both triangles        

ΔLKJ = ΔLMJ      ASA Congruence Postulate

Answer 2

Answer:

triangles AQB and AVB are congruent.

ΔLKJ ≅ ΔLMJ

Step-by-step explanation:

We have to prove that triangles LKJ and LMJ are congruent so let's

Consider triangles LKJ and LMJ;

∠KLJ=∠MLJ  {Given that LJ bisects ∠KLM}

∠KJL=∠MJL  {Given that LJ bisects ∠MJK}

LJ=LJ  {common side}

So using ASA, triangles AQB and AVB are congruent.

Hence it is proved that

ΔLKJ ≅ ΔLMJ