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)

The given figure shows a circle with center O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

A triangle ABC has ∠B = ∠C. Prove that :

(i) the perpendiculars from the mid-point of BC to AB and AC are equal.

(ii) the perpendicular from B and C to the opposite sides are equal.