Question

In ΔABC, D is the mid-point of AB and E is the mid-point of BC.

Calculate:
(i) DE, if AC = 8.6 cm
(ii) ∠DEB, if ∠ACB = 72°

Answer 1

In ΔABC,
Since D and E are the mid-point of AB and BC respectively

Therefore, by mid-point theorem DE || AC and DE = `(1)/(2)"AC"`

(i) DE = `(1)/(2)"AC" = (1)/(2) xx 8.6"cm"` = 4.3 cm

(ii) ∠DEB = ∠C = 72°.   ...(corresponding angles, since DE || AC)