State the four conditions under which a quadrilateral can be identified as a parallelogram.

If the opposite sides of a quadrilateral are equal, is it a parallelogram?

If the diagonals of a quadrilateral bisect each other, what can you conclude about the quadrilateral?

A quadrilateral has one pair of opposite sides that are both equal and parallel. What type of quadrilateral is it?

What special property must a parallelogram have to be classified as a rectangle?

Name two properties of the diagonals of a rectangle.

What is a rhombus? State one property of its diagonals that is not common to all parallelograms.

What special properties must a rectangle have to be classified as a square?

List two properties of the diagonals of a square.

In quadrilateral ABCD, the diagonals AC and BD intersect at O. If AO=OC and BO=OD, prove that ABCD is a parallelogram.

The midpoint of side BC of △ABC is T. A line through C parallel to AB meets AT produced at D. Prove that ABDC is a parallelogram.

AB and CD are two diameters of a circle with centre O. Prove that ACBD is a parallelogram.

Two parallelograms ABPQ and ABRS are drawn on the same base AB. Prove that QPRS is a parallelogram.

In parallelogram ABCD, the midpoints of the sides AB, BC, CD, and AD are P, Q, R, and S respectively. Prove that PQRS is a parallelogram.

In △ABC, the angle bisector of AB^C meets AC at P. A line through A parallel to BC meets BP produced at D such that BP=PD. Show that ABCD is a rhombus.