Math, asked by IronPanther123, 1 year ago

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.​

Answers

Answered by angryharsh9910
15

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]

Answered by llCuteChorill
3

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:

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