Question

a triangle ABC right angled at c a line through the midpoint of the hypotenuse a b and parallel to BC intersect AC at the show that D is the midpoint of AC

Answer 1

MID POINT THEOREM; The line joining the mid points of any two sides of a triangle is parallel to the third side and half of the third side.

D is the mid point of AC. 
Reason: by the converse of the mid point theorem since the line drawn is parallel to CB.