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

(i) In △ACD,

G is mid-point of CD and BG is parallel to AD,

∴ B is mid-point of AC (By converse of mid-point theorem).

By mid-point theorem,

BG = $\dfrac{1}{2}$AD = $\dfrac{1}{2}$ x 6 = 3 cm.

Hence, BG = 3 cm.

(ii) In △CDF,

G is mid-point of CD and GE || CF

∴ E is mid-point of FD (By converse of mid-point theorem).

By mid-point theorem,

GE = $\dfrac{1}{2}$CF

CF = 2GE

CF = 2(2.3) = 4.6 cm

Hence, CF = 4.6 cm.

(iii) From part (i)

B is mid-point of AC,

∴ AB = BC

Hence, AB = 2.4 cm

(iv) From part (ii),

E is mid-point of FD,

∴ ED = $\dfrac{1}{2}$FD = $\dfrac{1}{2}$ x 4.4 = 2.2 cm

Hence, ED = 2.2 cm