In a tringle ABC, AB = AC and bisector of angle A meets BC at D. Prove that :
(i) `DeltaABD cong DeltaACD` (ii) `AD` is perpendicular to BC.

ABC is a right triangle with AB = AC.If bisector of angle A meet BC at D then prove that BC =2 AD .

In triangle ABC, AB gt AC and D is any point on BC. Prove that, AB gt AD.

Given a DeltaABD in which AB=AD and AC bisects BD . Prove that : DeltaABC cong DeltaADC .

In a DeltaABC , BC = 9 cm, AC = 40 cm and AB = 41 cm. If bisector of angle A meets side BC at D then ratio of area of DeltaABD and DeltaABC is

DeltaABC and DeltaDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see figure). If AD is extended to intersect BC at P, show that : (i) DeltaABD cong DeltaACD (ii) DeltaABP cong DeltaACP (iii) AP bisects angleA as well as angleD (iv) AP is the perpendicular bisector of BC.

In a triangle ABC, angle bisector of angle BAC cut the side BC at D and meet the circumcircle of Delta ABC at E , then find AB .AC+DE. AE.

In a Delta ABC,AD is the bisector of the angle A meeting BC at D.If I is the in centre of the triangle,then AI:DI is equal to