ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively such that AB = BE and AD = DF. Prove that :

△ BEC ≅ △ DCF

In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced upto point R so that CR = BP.

Prove that QR bisects PC.

In the given figure, AB = PQ, BC = QR and median AM = median PN, then :

1. AC ≠ PR

2. BM ≠ QN

3. △ ABM ≅ △ PQN

4. △ ABC ≅ △ PQR

In triangles ABC and DEF, AB = DE and AC = EF, then to make these two triangles congruent, we must have :

1. BC = DF

2. ∠A = ∠E

3. any of (1) and (2)

4. none of (1) and (2)