Question

ABCD is a quadrilateral in which p,q,rand s are mid point of the side ab,bc,cd,da and ac is a diagonal show that sr parallel to ac and sr=1/2ac and pq=sr and pqrs is a parallelogram​

Answer 1

Answer:

1. In triangle ACD, S is the mid-point of AD and R is the mid-point of CD.

Them from mid-point theorem,

SR || AC and SR = 1/2 * AC

2. In triangle ABC, Pa nd Q are mid points of the sides AB and BC respectively.

Then from mid-point theorem,

PQ || AC and PQ = 1/2 * AC

Now PQ || AC and SR || AC

=> PQ || SR

Again PQ = PQ = 1/2 * AC and SR = 1/2 * AC

=> PQ || SR

3. Since PQ = SR and PQ || SR i.e.

One pair of opposite sides are equal and parallel.

So PQRS is a parallelogram.

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