ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.

Δ ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle.

Show that the angles of an equilateral triangle are 60° each.

Δ ABC and Δ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that

(i) Δ ABD ≅ Δ ACD

(ii) Δ ABP ≅ Δ ACP

(iii) AP bisects ∠A as well as ∠D

(iv) AP is the perpendicular bisector of BC