In △ ABC, D is mid-point of AB and E is mid-point of BC. Calculate :

(i) DE, if AC = 6.4 cm,

(ii) ∠DEB, if ∠ACB = 63°.

(i) By the Midpoint Theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of its length.

In △ ABC, since D is mid-point of AB and E is mid-point of BC.

So, DE = $\dfrac{1}{2}$ AC

DE = $\dfrac{1}{2}$ x 6.4 = 3.2 cm

Hence, the length of DE = 3.2 cm.

(ii) Since DE is parallel to AC (by mid-point theorem),

∠DEB = ∠ACB = 63° (∵ corresponding angles of parallel lines)

Hence, ∠DEB = 63°.