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
(i) D is the mid-point of AC
(ii) MD LAC
(iii) CM=MA = -AB​

Answer 1

Explanation:

In ∆AMD and ∆ABC ,

<ADM = <ACB

<AMD = <ABC

<A = <A ( COMMON ANGLE )

By AAA Criteria ,

∆ AMD IS CONGRUENT TO ∆ABC

SO,AD = DC

Therefore , D is the midpoint of AC