Question

Question 7 (i)
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
D is the mid-point of AC.

Answer 1

Given, ABC is a right-angled triangle.
$\angle C={90}^{\circ }$
And M is the mid-point of AB.
Also, DM || BC
In $\Delta$ ABC, BC || MD and M is mid - point of AB.
$\therefore$ D is the mid - point of AC. ( By converse of mid-point theorem)