Question

An angle bisector OX of ZAOB is drawn. A
point P on OX is joined to M and N on OB
and OA in such a way that OM=ON. Show
that AOPM SAOPN by SAS congruence condition :​

Answer 1

Answer:

Let M and N be the mid point of OA and OB. Let us join PM and PN. PM and PN are bisectors of OA and OB respectively

In AOMP and AONP, angle MOP = angle UP[ because OP is

bisector)

side OP is common to both triangles.

side OM = ON (we assumed)

hence AOMP and AONP are congruent. hence side PM = side PN