In Fig. 14.36, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF=2AB.

In Fig. 14.34, ABCD is a parallelogram in which ∠A=60°. If the bisectors of ∠A and ∠B meet at P, prove that AD=DP, PC=BC and DC=2AD.

In Fig. 14.35, ABCD is a parallelogram in which ∠DAB =75° and ∠DBC = 60°. Compute ∠CDB and ∠ADB.

Which of the following statements are true (T) and which are false (F)?

(i) In a parallelogram, the diagonals are equal.

(ii) In a parallelogram, the diagonals bisect each other.

(iii) In a parallelogram, the diagonals intersect each other at right angles.

(iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

(v) If all the angles of a quadrilateral are equal, it is a parallelogram.

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

(vii) If three angles of a quadrilateral are equal, it is a parallelogram.

(viii)If all the sides of a quadrilateral are equal it is a parallelogram.

In a parallogram ABCD, determine the sum of angles ∠C and ∠D.