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)

In quadrilateral ABCD, AB = AC and BD = CD, then AD bisects :

1. angle ADC

2. angle BAD

3. angle BAC

4. angle ABC

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.

In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the triangle PQR. If XS ⊥ QR and XT ⊥ PQ; prove that :

(i) △ XTQ ≅ △ XSQ

(ii) PX bisects angle P.