Question

It is given that $\angle$AMC is ${90}^{\circ }$, which of the following is/are true regarding the figure given below?

• A. M must be the midpoint of side BC.
• B. $\Delta AMN$ is a right angled triangle.
• C. AN is a median.
• D. AM is an altitude.

Answer 1

Answer: (B), (D)

The correct options are
B $\Delta AMN$ is a right angled triangle.
D AM is an altitude.

Since AM is perpendicular to side BC and passes through a vertex A, it acts as an altitude. An altitude may or may not pass through the midpoint.
Since, $\angle$AMC = ${90}^{\circ }$, $\Delta AMN$ is a right angled triangle.

In case of an equilateral triangle, altitude passes through the midpoint of the opposite side. So, it acts as both altitude and median.