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 AD=BC and angleDAB = angleCBA . Prove that: (i) triangleABD ~= triangleBAC (ii) BD = AC (iii) angleABD = angleBAC

ABCD is a quadrilateral. Is AB+BC+CD+DA>AC+BD?

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 a trapezium in which AB abs CD and AD = BC. Show that diagonal AC = diagonal BD

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

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

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

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Find the area of a quadrilateral ABCD in which AB = 3 cm , BC = 4 cm, CD = 4 cm , DA = 5 cm and AC = 5 cm.

In Fig. ABD is a triangle right angled at A and AC bot BD show that (i) AB^(2) =BC . BD , (ii) AC^(2) = BC . DC , (iii) AD^(2) = BD . CD