Question

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
MD $\perp$ AC .

Answer 1

Given, ABC is a right-angled triangle.

$\angle C={90}^{\circ }$

And M is the mid-point of AB.

Also, $MD\parallel BC$

Since, $MD\parallel BC$ and $CD$ is transversal.

$\therefore \angle ADM=\angle ACB$ ( Corresponding angles)

But $\angle ACB={90}^{\circ }$

$\therefore ADM={90}^{\circ }$

$\Rightarrow MD\perp AC$