**(a) In the figure (1) given below, ABCD is a parallelogram. E and F are mid-points of the sides AB and CO respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that**

**(i) ∆HEB = ∆HCF**

**(ii) GEHF is a parallelogram.**

**(b) In the diagram (2) given below, ABCD is a parallelogram. E is mid-point of CD and P is a point on AC such that PC = 14 AC. EP produced meets BC at F. Prove that**

**(i) F is mid-point of BC (ii) 2EF = BD**

**Solution:**

**More Solutions:**

- If P and Q are mid-points of OB and OC respectively.
- PQRS is a parallelogram
- The quadrilateral formed by joining the mid-points.
- Diagonals of ABCD are equal
- Prove that PQ ⊥ QR.
- The diagonals of a quadrilateral ABCD are perpendicular.
- Prove that AD and FE bisect each other.
- Find the perimeter of the parallelogram BDEF.
- Prove that B is mid-point of AF and EB = LF.
- Show that CR = 12 AC.