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

∠ADB = ∠BCA and ∠DAB = ∠CBA.

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 AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.

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.