Question

ps is an altitude of an isosceles triangle pqr in which pq = pr show that ps bisects p

Answer 1

PQ=PR is given
QM=MR by definition of midpoint
PM=PM by reflexive property

Triangle PQM is congruent to triangle PRM by SSS congruence.

Angles MPQ and MPR are congruent because they're corresponding angles of two congruent triangles.

PM bisects angle PQR by definition of angle bisector.