ABCD is a quadrilateral in which AD = BC and `angle DAB =angle CBA` (see Fig. 7.17). Prove that (i) `triangle ABD cong triangle BAC` (ii) BD = AC (iii) `angle ABD = angle BAC`.

ABCD is a quadrilateral in which AD=BC and angleADB=angleCBA . Prove that: BD=AC

ABCD s a trapezium in which AB||CD and AD=BC angleC=angleD

In quadrilateral ACBD, AC = AD and AB bisects angle A (see Fig. 7.16). Show that triangle ABC cong triangle ABD . What can you say about BC and BD?

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

In the fig. ABCD is a quadrilateral in which AB is the largest and CD is the shortest side. Prove that: angleD>angleB

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB (see Fig. 8.14). Show that (i) angle DAC = angle BCA and (ii) ABCD is a parallelogram.

Line l is the bisector of an angle angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of angle A (see Fig. 7.20). Show that: (i) triangle APB cong triangle AQB (ii) BP = BQ or B is equidistant from the arms of angle A .

In the fig. :ABCD is a quadrilateral in which AD=AB and BC=DC. Prove that AC bisects angleA=angleC

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.If angleDBC = 70^@ and angle BAC = 30^@ find angleBCD

In the fig. :ABCD is a quadrilateral in which AD and BC=DC. Prove that AC is the perpendicular bisector of BD.