Question

The diagonals of a parallelogram PQRS intersect at O. A line through O intersects PQ at M and RS at N,
prove that OM = ON.​

Answer 1

In ∆OMP and ∆ONR,

Angle POM = Angle RON. [Vertical opp. Angles]

OP = OR [diagonals of a parall....grm bisects each other]

Angle OPM = Angle ORN [ PQ Parallel to RS]

Therefore, ∆OMP Congruent to ∆ONR [ASA]

Therefore, OM = ON [By CPCT]

Answer 2

Answer:

In ∆OMP and ∆ONR,

Angle POM = Angle RON. [Vertical opp. Angles]

OP = OR [diagonals of a parall....grm bisects each other]

Angle OPM = Angle ORN [ PQ Parallel to RS]

Therefore, ∆OMP Congruent to ∆ONR [ASA]

Therefore, OM = ON [By CPCT]

Step-by-step explanation: