ABCD is a rectangle in which diagonal AC bisects A as well as C. Show that :
ABCD is a square

ABCD is a rectangle in which diagonals AC bisects angleA as well as angleC , Show that ABCD is a square diagonal BD bisects angleB as well as angleD

ABCD is a rhombus. Show that diagonal AC bisects A as well as C and diagonal BD bisects B as well as D.

ABCD is a rhombus Show that diagonal AC bisects angleA as well as angleC and diagonal BD bisects angleB as well as angleD .

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

ABCD is a trapezium in which AB abs CD and AD = BC. Show that DeltaABC~=DeltaBAD

Diagonal AC of a parallelogram ABCD bisects A. Show that ABCD is a rhombus.

ABCD is a rectangle AC is diagonal. Find the nature of DeltaACD . Give reasons.

Parallelogram ABCD and rectangle ABEF are on the base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar (ACB) = ar (ACF) (ii) ar (AEDF) = ar (ABCDE)

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD "||" BA as shown in the figure. Show that (i) angleDAC = angleBCA (ii) ABCD is a parallelogram