Question

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

Answer 1

(i) In Δ ACD,

G is the mid-point of CD

BG || AD as m || n

Here B is the mid-point of AC and BG = ½ AD

So we get

BG = ½ × 6 = 3 cm (1 Mark)

(ii) In Δ CDF

G is the mid-point of CD

GE || CF as m || l

Here E is the mid-point of DF and GE = ½ CF

So we get

CF = 2GE

CF = 2 × 2.3 = 4.6 cm (1 Mark)

(iii) From (i)

B is the mid-point of AC

AB = BC

We know that

BC = 2.4 cm

So AB = 2.4 cm (1 Mark)

(iv) From (ii)

E is the mid-point of FD

ED = ½ FD

We know that

FD = 4.4 cm

ED = ½ × 4.4 = 2.2 cm (1 Mark)