Question

ABC is a triangle right angled at C. Aline through the mid-point M
of hypotenuse AB and parallel to BC Intersects AC at D. Show that
D is the midpoint of AC.
MD perpendicular bisector of AC
CM=MA=1/2AB​

Answer 1

Answer:

Heya,

GIVEN:-

ABC is a triangle right angled at C. A line passing through mid points M of hypotenuse AB and parallel to BC intersects AC at D

TO PROVE:-

(i) D is the midpoint of AC

(ii) CM=MA=1/2AB

PROOF:-

(i) M is a mid point of AB, DM||CB Therefore, D is a midpoint of AC

(ii) Construction:-

Join CM

In, ΔADM, ΔCDM

AD=DC => S

∠1= ∠3 => A

DM=DM [common] => S

∴ ΔADM ≅ ΔCDM [SAS ≅] ∴CM=AM=1/2AB [cpct]

Hope my answer helps you :)