1. In the below figure, ABCD is a parallelogram and DAB = 60^{0}. If the bisector AP and BP of angles A and B respectively meet P on CD. Prove that P is the midpoint of CD.

2. In the below given figure, ABCD is a parallelogram and E is the midpoint of side BC, DE and AB when produced meet at F. Prove that AF = 2AB.

3. ABC is right angle at B and P is the midpoint of AC and Q is any point on AB. Prove that (i) PQ AB (ii) Q is the midpoint of AB (iii) PA = 1/2AC

4. The diagonals of a parallelogram ABCD intersect at O. A line through O intersects AB at X and DC at Y. Prove that OX = OY.

5. ABCD is a parallelogram. AB is produced to E so that BE = AB. Prove that ED bisects BC.

6. If ABCD is a quadrilateral in which AB || CD and AD = BC, prove that A = B.

7. Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD.

8. In quadrilateral ABCD, A + D = 1800. What special name can be given to this quadrilateral?

9. All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

10. In ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.