Question

The diagonal BD of a parallelogram ABCD is bisected at O. Through O a line is drawn, cutting BC and AD at
P and Q respectively. Prove that OP=OQ and BPDQ is a parallelogram​

Answer 1

Answer:

In ∆OPD AND ∆QBO

OP=OB(GIVEN)

ANGLE OPQ =ANGLE OQB(ALTERNATE)

ANGLE POD =ANGLE OQB(VERTICALLY OPPOSITE)

∆OPD CONGRUENT TO ∆QOB(by AAS CRITERIAN)

OP=OQ(CPCTC)

PD=BQ(CPCTC).

opposite side of parallelogram are equal and hence BPDQ IS PAARALELOGRAM