Sita marks the midpoints of the four sides of any quadrilateral ABCD and joins them in order to form PQRS. The mid-point theorem shows PQ is parallel and equal to half of AC, and SR is parallel and equal to half of AC. Why is PQRS always a parallelogram?

Question

Accepted Answer

PQ and SR are equal and parallel, one pair of opposite sides equal and parallel. Both PQ and SR equal half of AC and are parallel to AC, so PQ is equal and parallel to SR. One pair of opposite sides equal and parallel makes PQRS a parallelogram.

Sita marks the midpoints of the four sides of any quadrilateral ABCD and joins them in order to form PQRS.
The mid-point theorem shows PQ is parallel and equal to half of AC, and SR is parallel and equal to half of AC.
Why is PQRS always a parallelogram?

Step-by-Step Solution

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More Class 9 Conditions for a Parallelogram practice

Sita marks the midpoints of the four sides of any quadrilateral ABCD and joins them in order to form PQRS.The mid-point theorem shows PQ is parallel and equal to half of AC, and SR is parallel and equal to half of AC.Why is PQRS always a parallelogram?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Conditions for a Parallelogram practice

Sita marks the midpoints of the four sides of any quadrilateral ABCD and joins them in order to form PQRS.
The mid-point theorem shows PQ is parallel and equal to half of AC, and SR is parallel and equal to half of AC.
Why is PQRS always a parallelogram?