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

(i) Given: The straight line l, m and n are parallel to each other.

G is the mid point of CD.

In Δ ACD,

G is the mid point of CD and BG ∥ AD as m ∥ n.

⇒ BG = $\dfrac{1}{2}$ AD (Converse of midpoint theorem)

= $\dfrac{1}{2}$ x 12

= 6 cm

Hence, the value of BG = 6 cm.

(ii) In Δ CDF,

G is the mid point of CD and GE ∥ CF as m ∥ l.

⇒ GE = $\dfrac{1}{2}$ CF (Converse of midpoint theorem)

⇒ 4.6 = $\dfrac{1}{2}$ x CF

⇒ CF = 4.6 x 2

⇒ CF = 9.2

Hence, the value of CF = 9.2 cm.

(iii) In Δ ACD,

G is the mid point of CD and BG ∥ AD as m ∥ n.

⇒ B is the mid point of AC (Converse of midpoint theorem)

⇒ AB = BC

⇒ AB = 4.8 cm

Hence, the value of AB = 4.8 cm.

(iv) In Δ CDF,

E is the mid point of FD and CF ∥ GE as m ∥ l.

⇒ ED = $\dfrac{1}{2}$ FD (Converse of midpoint theorem)

= $\dfrac{1}{2}$ x 8.8

= 4.4

Hence, the value of ED = 4.4 cm.