Question

please help me........

Answer 1

In the given triangle ABC:

= > P and Q are the mid-points of AB and AC.

By mid-point theorem, we get

= > PQ || AC

= > PQ = (1/2) AC

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In the given triangle ADC:

= > S and R are the mid-points of AD and DC.

By mid-point theorem, we get

= > SR || AC

= > SR = (1/2) AC

So,

PQ || SR and PQ = SR.

Hence, PQRS is a parallelogram.

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In rectangle ABCD,

AD = BC[Opposite sides]

= > (1/2)AD = (1/2)BC

= > AS = BQ.

In triangle APS and BPQ

AP = BP[P is the midpoint of AB]

<PAS = <PBQ

PS = PQ

PQ = RS = PS = RQ

Here, all sides are equal.

Therefore, PQRS is a rhombus.

Hope it helps!