If the diagonals of a quadrilateral PQRS bisect each other at right angles, then the quadrilateral PQRS must be a

1. parallelogram

2. rectangle

3. rhombus

4. square

Which of the following statement is true for a parallelogram?

1. Its diagonals are equal.

2. Its diagonals are perpendicular to each other.

3. The diagonals divide the parallelogram into four congruent triangles.

4. The diagonals bisect each other.

A quadrilateral in which the diagonals are equal and bisect each other at right angles is a

1. rectangle which is not a square

2. rhombus which is not a square

3. kite which is not a square

4. square

In the adjoining figure, ABCD is a parallelogram. CB is produced to E such that BE = BC. Prove that AEBD is a parallelogram.