Q18 of 168 Page 4

In right-angled triangle ABC in which, if D is the mid-point of BC, prove that .

We have

∠C=90 and D is the midpoint of BC

In ABC

AB²=AC²+BC²

AB²=AC²+ (2CD)²

AB²=AC²+4CD²

AB²=AC²+4(AD²-AC²)

AB²=AC²+4AD²-4AC²

AB²=4AD²-3AC²

In an acute-angled triangle, express a median in terms of its sides.

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

In Fig. 4.220, D is the mid-point of side BC and . If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that:

(i) (ii)

(iii)

In Fig. 4.221, and segment , show that

(i)

(ii)