Question

triangle ABC is right angled at C. A line through the midpoint M of hypotenuse AB and parallel to BC intersects Ac at D. Show that MD perpendicular to AC

Answer 1

Given: A △ABC , right - angled at C. A line through the mid - point M of hypotenuse AB parallel to BC intersects AC at D.

Since ∠BCA = 90°

and MD | | BC [given]

⇒ ∠MDA = ∠BCA

= 90° [corresp ∠s]

⇒ MD | AC