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In Parallelogram Pqrs, L is Mid-point of Side Sr and Sn is Drawn Parallel to Lq Which Meets Rq Produced at N and Cuts Side Pq at M. Prove that M is the Mid-point of Pq.

Question

In parallelogram PQRS, L is mid-point of side SR and SN is drawn parallel to LQ which meets RQ produced at N and cuts side PQ at M. Prove that M is the mid-point of PQ.

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Solution

In ΔNSR

MQ = `(1)/(2)"SR"`
But L is the mid-point of SR and SR = PQ ...(sides of a parallelogram)

MQ = `(1)/(2)"PQ"`
MQ = PM = LS = LR
Therefore, M is the mid-point of PQ.

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Theorem of Midpoints of Two Sides of a Triangle

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Q 4 Q 3.3 Q 5.1

Chapter 11: Midpoint and Intercept Theorems - Exercise 15.1

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Frank Mathematics Part 1 [English] Class 9 ICSE

Chapter 11 Midpoint and Intercept Theorems
Exercise 15.1 | Q 4

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In Parallelogram Pqrs, L is Mid-point of Side Sr and Sn is Drawn Parallel to Lq Which Meets Rq Produced at N and Cuts Side Pq at M. Prove that M is the Mid-point of Pq.

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In Parallelogram Pqrs, L is Mid-point of Side Sr and Sn is Drawn Parallel to Lq Which Meets Rq Produced at N and Cuts Side Pq at M. Prove that M is the Mid-point of Pq.

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