In the adjoining figure, AB = AC and D is the midpoint of BC. Use SSS rule of congruency to show that

(i) △ABD ≅ △ACD

(ii) AD is bisector of ∠A

(iii) AD is perpendicular to BC.

In the adjoining figure, AB = DC and AB || DC. Prove that AD = BC.

In the adjoining figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that

(i) △ABD ≅ △BAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC

In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that

(i) △ACE ≅ △DBF

(ii) AE = DF.