Question

ABC is a triangle , right angled at C . A line through the midpoint M of hypoteneuse AB and || to BC intersect at D . Show •DC midpoint of AC
•MD perpendicular AC
• CM = MA = half AB

Answer 1

Answer:

Step-by-step explanation:

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 :)