Question

15. In the adjoining figure, ABCD and PQBA are two parallelograms.
Prove that :
(i) DPQC is a parallelogram.
(ii) DP = CQ.
(iii) ADAP = ACBQ.
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Answer 1

Consider △RSC and △PQB

From the figure we know that RC∥PB and ∠CRS and ∠BPQ and ∠RSC and ∠PQB are corresponding angles

It can be written as

∠CRS=∠BPQ and ∠RSC=∠PQB

We know that the opposite sides of parallelogram are equal

SC=QB

By AAS congruence criterion

△RSC≃△PQB

So we get

Area of △RSC = Area of △PQB

Therefore, it is proved that ar(△RSC)=ar(△PQB).

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Answer 2

Answer:

Consider △RSC and △PQB

From the figure we know that RC∥PB and ∠CRS and ∠BPQ and ∠RSC and ∠PQB are corresponding angles

It can be written as

∠CRS=∠BPQ and ∠RSC=∠PQB

We know that the opposite sides of parallelogram are equal

SC=QB

By AAS congruence criterion

△RSC≃△PQB

So we get

Area of △RSC = Area of △PQB

Therefore, it is proved that ar(△RSC)=ar(△PQB).

Step-by-step explanation:

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