Another Condition for a Quadrilateral to Be a Parallelogram

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

(i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.

The following statement are true  and false .

If three sides of a quadrilateral are equal, it is a parallelogram .

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that

(i) ΔAPB ≅ ΔCQD

(ii) AP = CQ

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

The following statement are true  and false. 

In a parallelogram, the diagonals bisect each other.

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

The following statement are true  and false .

In a parallelogram, the diagonals are equal

If the diagonals of a parallelogram are equal, then show that it is a rectangle.