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 of AC

(ii) MD is perpendicular to AC

(iii) CM=MA= 1/2 AB

Answer 1

may this answer help you

Answer 2

Solution:-

In ∆ABC, we have

M is the midpoint of AB and MD||BC

D is the midpoint of AC {by converse of midpoint theorem}

Now

MP||BC

<MDC+<BCD=180°

<MDC+90°=180°

<MDC=90°

Thus;MD perpendicular AC

Join MC

In ∆MDA and ∆MDC we have

DA=DC

<MDA=<CDM

MD=MD

∆MDA~∆MDC {S.A.S}

And so MA=MC

Now M is the midpoint of AB

MA=MC=1/2AB