Question

In the adjoining figure, ABCD is a square and M is the mid-point of AB. PQ is any line segment through
M which meets AD at P and CB produces till Q. Prove that M is also mid-point of PQ

Answer 1

Answer:

ΔPAMandΔBMQ

∠PMA=∠BMQ=α

AM=MB

∠PAM=∠MBQ=90

∘

InΔCPQ

LM⊥PQ

PM=MQ

CP=CQ(isoscelesΔCPQ)

CQ=CB+BQ

CQ=AB+BQ

So,BA=BQ