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.
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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]
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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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