The given figure shows two isosceles triangles ABC and DBC with common base BC. AD is extended to intersect BC at point P. Show that:
` Delta ABD = Delta ACD `
(ii) `Delta ABP = Delta ACP `
(iii) AP bisects ` angle BDC `
(iv) AP is perpendicular bisector of BC.

DeltaA B C and DeltaD B C are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that (i) \ DeltaA B D~=DeltaA C D (ii) DeltaA B P~=DeltaACP (iii) AP bisects ∠ A as well as ∠ D (iv) AP is the perpendicular bisector of BC

ABC is an equilateral triangle .If AD bisects angle A, Prove that AD is perpendicular bisector of BC .

Construct two isosceles triangles ABC and DBC, with common base BC and the points A and D on opposite sides of BC, given that BC = 8 cm, AB = AC = 4.5 cm, and DB = DC = 5 cm.

The given figure shows an isosceles triangle ABC inscribed in a circle such that AB=AC. If DAE is a tangent to the circle at point A, prove that DE is parallel to BC.

Triangles ABC and DBC are two isosceles triangles on the same base BC and their vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that: Delta ABP ~= Delta ACP

In Delta ABC, AB =AC and D is a piont in side BC such that AD bisect angle BAC. Show that AD is perpendicular bisector of side BC.

The given figure shows an equilateral triangles ABC and D is point in AC. Prove that : (i) AD lt BD (ii) BC gt BD

In isosceles triangle ABC, D is a point on the base BC produced. Prove that AD gt AB .

In a triangle ABC, D is mid-point of BC, AD is produced upto E so that DE = AD. Prove that : (i) Delta ABD and Delta ECD are congruent. (ii) AB = EC (iii) AB is parallel to EC.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F. Prove that : F is equidistant from AB and AC.