Question

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

Answer 1

ΔLKJ = ΔLMJ

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

triangles AQB and AVB are congruent.

ΔLKJ ≅ ΔLMJ

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