Question

In the given figure, ABCD and AEFD are two parallelograms. Prove that

(i) PE = FQ

(ii) ar (Δ APE): ar (ΔPFA) = ar Δ (QFD) : ar (Δ PFD)

(iii) ar (Δ PEA) = ar (Δ QFD).

Answer 1

Given: ABCD and AEFD are two parallelograms

To prove:

(i) PE = FQ

(ii)

(iii)

Proof: (i) and (iii)

In ΔAPE and ΔDQF

Therefore

, and

(ii) ΔPFA and ΔPFD are on the same base PF and between the same parallels PQ and AD.

From (1) and (2) we get