In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :

(i) AD is perpendicular to FE.

(ii) AD and FE bisect each other.

In trapezium ABCD, AB // DC. M is mid-point of AD and N is mid-point of BC.

(i) If AB = 8 cm and DC = 11 cm, find MN.

(ii) If AB = 5.7 cm and MN = 6.2 cm, find DC.

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

(i) BG, if AD = 12 cm

(ii) CF, if GE = 4.6 cm

(iii) AB, if BC = 4.8 cm

(iv) ED, if FD = 8.8 cm