Question

In $\Delta ABC$; $BM\perp AC$ and $CN\perp AB$;

Then, $\frac{AB}{AC}=\frac{BM}{CN}=\frac{AM}{AN}$

• A. True
• B. False

Answer 1

The correct option is A

True

In $\Delta ABC$,

$BM\perp AC$ and $CN\perp AB$

In $\Delta AMB$ and $\Delta ANC$

$\angle A=\angle A$ (Common)

$\angle M=\angle N$ (each ${90}^{\circ }$)

$\therefore \Delta AMB\sim \Delta ANC$ (AA axiom)

$\therefore \frac{AB}{AC}=\frac{BM}{CN}=\frac{AM}{AN}$

(Corresponding sides are proportional)