Question

D is the mid-point of the base BC of triangle ABC. DM and DN are perpendiculars on AB and AC respectively. If DM = DN, then the triangle is

• A. an isosceles triangle
• B. an equilateral triangle
• C. a right-angled triangle
• D. a scalene triangle

Answer 1

The correct option is A an isosceles triangle

In $△DMB$ and $△DNC$,

BD = DC [D is midpoint of BC]

DM = DN [given]

$\angle DMB$ = $\angle DNC$ [equal to ${90}^{\circ }$ (given)]

$\therefore$ $△DMB\cong △DNC$ [ RHS Congruency Rule ]

By CPCT, $\angle MBD=\angle NCD$.

$\Rightarrow$ AB = AC

$\Rightarrow \Delta ABC$ is an isosceles triangle.