Please show work

Question

2.  Use congruent triangles to complete a two-column proof of the following.

Remember to show all markings on the diagram for part of your work.

Given: K is the midpoint of PN and JO

Prove: PO || JN and JP || NO

Answer 1

In ΔPKO and ΔJKN length of PK= length of KN....given

length of KJ=length of KO.....given∠

measure of ∠PKO=measure of ∠JKN........vertical angles are equalΔ

ΔPKO ≅ ΔJKN SAS

measure of ∠POK=measure of ∠NJO......corresponding parts of congruent triangles

PO is parallel to JN ....alternate-interior angles are equal

An exactly similar argument on the other 2 triangles will get you PJ parallel to ON