In `triangle` ABC, AB = AC and the bisector of `angle A lt` intersects BC at D. Prove that, ( 1 )`triangle ADB = triangle ADC ( 2 ) angle ABC = angle ACB`

triangle ABC and triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that, ( i ) triangle ABD = triangle ACD (ii) triangle ABP = triangle ACP (iii) AP bisects angle A as well as angle D. (iv) AP is the perpendicular bisector of BC

In triangle ABC, AB = AC and angle A = 36^(@) . The bisector of angle C intersects AB at D. Find the measures of required angles to prove that AD = BC

ABCD is a quadrilateral in which AD = BC and angle DAB = angle CBA (see the given figure). Prove that ( i ) triangle ABD = triangle BAC, ( ii) BD = AC and (iii) angle ABD = angle BAC

In a triangle ABC, sin A- cos B = Cos C , then angle B is

In triangle ABC, AC gt AB . AB is extended to P and AC is extended to Q. Prove that, angle PBC lt angle QCB .

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

In quadrilateral ACBD. AC = AD and AB bisects angle A (see the given figure). Show that triangle ABC = triangle ABD . What can you say about BC and BD?

In triangle ABC , the bisector AD of angle A is perpendicular to side BC (see the given figure). Show that AB = AC and triangle ABC is isosceles.

In triangle ABC, the bisectors of angle B and angle C intersect at I. A line drawn through I and parallel to BC intersects AB at P and AC at Q. Prove that PQ = BP + CQ.

ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CBD.