Points A and B are on the opposite edges of a pond as shown in Fig. 6.56. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.

Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC.

(i) Is ∆ABC ≅ ∆DCB? Why?

(ii) Is AB = DC? Why?

(iii) Is AC = DB? Why?

In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT.

(i) Is ∆QSR ≅ ∆RTQ? Give reasons.

(ii) Is ∠PQR = ∠PRQ? Give reasons.

Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.

The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground, (a) Find the length of the ladder. (b) If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its top reach?