Question

In the given figure, PQ ∥ SR ∥ MN, PS ∥ QM and SM ∥ PN. Prove that: ar. (SMNT) = ar. (PQRS).

Answer 1

SM ∥ PN
⇒ SM ∥ TN
Also, SR ∥ MN
⇒ ST ∥ MN
Hence, SMNT is a parallelogram.
SM ∥ PN
⇒ SM ∥ PO
Also, PS ∥ QM
⇒ PS ∥ OM
Hence, SMOP is a parallelogram.
Now, parallelograms SMNT and SMOP are on the same base SM and between the same parallels SM and PN.
∴ A(parallelogram SMNT) = A(parallelogram SMOP) ….(i)
Similarly, we can show that quadrilaterals PQRS is a parallelogram.
Now, parallelograms PQRS and SMOP are on the same base PS and between the same parallels PS and QM.
∴ A(parallelogram PQRS) = A(parallelogram SMOP) ….(ii)
From (i) and (ii), we have
A(parallelogram SMNT) = A(parallelogram PQRS).