Question

In Fig. explain how one can find the breadth of the river without crossing it.

Answer 1

Let AB be the breadth of the river. Mark any point M on the bank which B is situated. Let O be the mid-point of line segment BM. Join AO and produce it to N such that AO = ON. Join M and N.

Now, in $△$s AOB and NOM, we have

AO = ON [By construction]

$\angle$AOB = $\angle$MON [Vertically opposite angles]

BO = OM [O is the mid-point of BM]

So, By SAS criterion of congruence

$△$AOB $\cong$ $△$NOM

Therefore, By CPCT AB = MN

Hence, breadth of river is equal to MN.