In the adjoining figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that

(i) △APC ≅ △AQB

(ii) CP = BQ

(iii) ∠ACP = ∠ABQ.

In the adjoining figure, AD = BC and BD = AC. Prove that:

∠ADB = ∠BCA and ∠DAB = ∠CBA.

"If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent." Is the statement true? Why?

In the adjoining figure, AB = AC and AP = AQ. Prove that

(i) △APC ≅ △AQB

(ii) CP = BQ

(iii) ∠APC = ∠AQB.