Question

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 .show that:
1) D is mid point of AC

2) CM=MA=HALF 0F AB

Answer 1

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 :)

Regards,
Shobana

Answer 2

This is step by step explantion.

Mark it as. a brainlist answer