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

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that (i) DeltaABD ~= DeltaACE (ii) AB = AC i.e., ABC is an isosceles triangle.

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

If in a cyclic quadrilateral ABCD, AB=DC , then prove that AC=BD

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

In the the cyclic quadrilateral ABCD,AB =CD . Prove that AC= BC

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that, (i) AD bisects BC (ii) AD bisects /_ A.

In the quadrilateral ABCD , AD = BC and angleBAD = angleABC . Prove that the quadrilateral is an isosceles trapezium.

If in the cyclic quadrilateral AB||CD , then prove that AD =BC and AC=BD.

A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC bot BD , angleCAD = theta , then the angle angleABC equals___

In the cyclic quadrilateral ABCD , the diagonal BD bisects the diagonal AC . Prove that ABxxAD=CBxxCD .