In the figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :

(i) ∠EFG = 90°

(ii) The line drawn through G and parallel to FE bisects DA.

In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate :

(i) BG if AD = 6 cm

(ii) CF if GE = 2.3 cm

(iii) AB if BC = 2.4 cm

(iv) ED if FD = 4.4 cm

In the adjoining figure, ABCD is a rectangle in which AB = 6 cm and AD = 8 cm. If P and Q are mid-points of the sides BC and CD respectively, then the length of PQ is

1. 7 cm

2. 5 cm

3. 4 cm

4. 3 cm

D and E are mid-points of the sides AB and AC of △ABC and O is any point on the side BC. O is joined to A. If P and Q are mid-points of OB and OC respectively, then DEQP is

1. a square

2. a rectangle

3. a rhombus

4. a parallelogram