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

ABCD is a quadrilateral in which AB //// DC and AD //// BC. Find /_b,/_c and /_d

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.

ABCD is quadrilateral in which AB |\| DC and AD |\| BC . Find angle b, angle c, angle d .

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

In quadrilateral ABCD, AB = BC = CD = AD and AC ne BD then it is a .....

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

In a quadrilateral ABCD, angleB = 90^0 , AD^2 = AB^2 + BC^2 + CD^2 . Prove that angle ACD = 90 ^0 .

ABD is a Triangle right angle at A and AC bot BD . Show that (i) AB^2=BC.BD (ii) AD^2=BD.CD (iii) AC^2=BC.DC

ABCD is a trapezium in which AB||DC the diagonals AC and BD are intersecting at E. IF DeltaAED is similar to DeltaBEC , then prove that AD=BC.

In triangle ACB , angle C = 90^@ and CD bot AB . Prove that BC^2/AC^2 = BD/AD .