Answer:
In \[\Delta \text{ }ABM\text{ }and\text{ }\Delta \text{ }ACN,\]
\[\angle AMB\text{ }=\text{ }\angle ANC\] [Since, BM ⊥ AC and CN ⊥ AB]
\[\angle BAM\text{ }=\angle CAN\] [Common angle]
Thus, \[\vartriangle ABM\text{ }\sim\text{ }\vartriangle ACN\]by \[AA\]rule for similitude
In this way, by relating sides of comparative triangles we have