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

In the figure, if BD bot AC and CE bot AB , prove that (i) Delta AEC~ Delta ADB " " (ii) (CA)/(AB)=(CE)/(DB)

ABCD is trapezium with AB || DC. The diagonal AC and BD intersect at E . If Delta AED ~ Delta BEC . Prove that AD = 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 quadrilateral ABCD, AB=AD, AC bisects angleA . Prove DeltaABC~ADC .

Find the area of a quadrilateral ABCD in which AB = 8 cm, BC = 6 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm and |__ulB = 90^(@) .

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

In squareABCD is a quadrilateral. M is the midpoint of diagonal AC and N is the midpoint of diagonal BD. Prove that : AB^(2)+BC^(2)+CD^(2)+DA^(2)=AC^(2)=AC^(2)+BD^(2)+4MN^(2).

Two forces vec A B and vec A D are acting at vertex A of a quadrilateral ABCD and two forces vec C B and vec C D at C prove that their resultant is given by 4 vec E F , where E and F are the midpoints of AC and BD, respectively.

ABCD is quadrilateral with AB parallel to DC. A line drawn parallel to AB meets AD at P and BC at Q. prove that (AP)/(PD) = (BQ)/(QC)

In the adjoining figure "seg "Cebot" side " AB, " seg" AD bot" side " BC. Prove that (i) DeltaAEP~DeltaCDP (ii) DeltaAEP~DeltaADB