Question

In the adjoining figure, ABCD and BQSC are two parallelograms. Prove that ar (△ RSC) = ar (△ PQB).

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).