In the adjoining figure, explain how one can find the breadth of the river without crossing it.
Given: AB ⊥ BO and NM ⊥ OM
In ∆ABO and ∆NMO,
∠OBA = ∠OMN
OB = OM …O is mid point of BM
∠BOA = ∠MON …vertically opposite angles
Thus by AAS property of congruence,
∆ABO ≅ ∆NMO
Hence, we know that, corresponding parts of the congruent triangles are equal
∴ AB = MN
Hence, we can calculate the width of the river by calculating MN