In quadrilateral ABCD, BA = BC and DA = DC. Prove that BD bisects `angle` ABC as well as `angle` ADC.

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 cyclic quadrilateral ABCD. Diagonals AC and BD intersect at P. If angle DBC = 70^(@) and angle BAC = 30^(@) , find angle BCD.

ABCD is a quadrilateral in which AD = BC and /_ DAB = /_ CBA Prove that (i) DeltaABD ~= DeltaBAC (ii) BD = AC (iii) /_ ABD = /_ BAC

AB and CD are respec­tively the smallest and longest sides of a quadrilateral ABCD (see th e given figure). Show that angle A gt angle C and angle B gt angle D

In quadrilateral ACBD, AC = AD and AB bisects /_A Show that DeltaABC~= DeltaABD . What can you say about BC and BD?

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 cyclic quadrilateral ABCD, angle A - angle C =20^(@). Then, angle A= ..........

In quadrilateral ABCD, AM and CN are altitudes on diagonal BD drawn from A and C respectively .Prove that ar(ABCD)= 1/2 BD(AM+CN)

In cyclic quadrilateral ABCD, angle A = 70^(@) and angle B + angle X = 160^(@). Then, angle B= ………

In quadrilateral ABCD, AB = 9 cm, BC = 12 cm, CD = 8.5 cm, DA = 8.5 cm and AC = 15 cm. Find the area of quadrilateral ABCD.