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

In quadrilateral ABCD, AB=DC and AD=BC. Prove that the sides AB and DC are parallel to each other.

The diagonals of quadrilateral ABCD, AC and BD intersects at O. Prove that if BO = OD then the triangles ABC and ADC are equal in area.

ABCD is a quadrilateral in which AB=BC and AD =CD ,Show that BD bisects boht the angle ABC and ADC

ABCD is a quadrilateral in which AB||DC and AD = BC. Prove that angleA=angleB and angleC= angleD .

In a quadrilateral ABCD, OA and OB are the angle bi- sectors of angleDABandangleCBA . If ∠ADC=70 and ∠ BCD= 80 then find the angle AOB

In a cyclic quadrilateral ABCD, AB = BC, AD = DC, AC_|_BD, angleCAD=theta . Then angleABC will be-

In quadrilateral ABCD,side DC is largest. Show that AB+AD>DC-BC .

Three statements are given below: I. In a rectangle ABCD, the diagonal AC bisects angle A as well as angle C. II. In a square ABCD, the diagonal AC bisects angle A as well as angle C. III. In a rhombus ABCD, the diagonal AC bisects angle A as well as angle C. Which is true?

In triangle ABC,AD and a Earn ABCD is a rhombus,AB is produced In the figure bisector of B and D of quadrilateral ABCD meet CO and AB produced and Q respectively.Prove that angle P t angle Q (angle ABC t le ADC).A

ABCD is a convex quadrilateral with AB = 3, BC = 5 and CD = 7. If the bisectors of the four internal angles are concurrent, find the value of (AB + BC + CD + DA)/(DA).