ABCD is a rectangle in which diagonal AC bisects `/_A` as well as `/_C`. Show that:
ABCD is a square.

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

ABCD is a trapezium in which AB||DC and its diagonals intersects each other at the point O. Show that (AO)/(BO)=(CO)/(DO) .

Diagonal AC of a parallelogram ABCD bisects /_A (see the given figure), show that ABCD is a rhombus.

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

ABC is an isosceles triangle in which AB=AC bisects exterior angle PAC and CD||AB (See the given figure ). Show that ABCD is a parallelogram

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

ABC is an isosceles triangle in which AB=AC bisects exterior angle PAC and CD||AB (See the given figure ). Show that /_DAC = /_BCA

In the figure, ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

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