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

In a quadrilateral ABCD, AB = CD and angle B = angle C . Prove that AD is parallel to BC.

In a quadrilateral ABCD, vec(AB) + vec(DC) =

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

In a quadrilateral ABCD, it is given that AB |\|CD and the diagonals AC and BD are perpendicular to each other. Show that AD.BC >= AB. CD .

ABCD is a cyclic quadrilateral , Sides AB and DC produced meet at point E , whereas sides BC and AD produced meet at point F. If angle DCF : angle F : angle E =3 : 5 : 4 find the angles of the cyclic quadrilateral ABCD.

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

In quadrilateral ABCD, AB is the shortest side and DC is the longest side. Prove that : (i) angleB gt angleD (ii) angleA gt angleC

ABCD is a quadrilateral in which AB=AD . The bisector of BAC and CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD.

In trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC. Prove that : AB + DC = 2EF.

Figure shows a part of an electric circuit. ABCD is a rectangular loop made of uniform wire. The length AD= BC = 1 cm. The sides AB and DC are long as compared to the other two sides. Find the magnetic force per unit length acting on the wire DC due to the wire AB if the ammeter reads 10A.