# Q: 7  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                (i) D is the mid-point of AC

Given: 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.

To prove :D is mid point of AC.

Proof: In $\triangle$ABC,

M is mid point of AB.                (Given)

DM || BC            (Given)

By converse of mid point theorem,

D is the mid point of AC.

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