Question

In the given figure,L and M are the mid-points of AB and BC respectively.

(i) If AB=BC,prove that AL=MC.

(ii) If BL=BM,prove that AB=BC.

Answer 1

(i) It is given that L is the mid-point of AB.

∴ AL = BL = 1/2 AB .....(1)

Also, M is the mid-point of BC.

∴ BM = MC = 1/2 BC .....(2)

AB = BC (Given)
⇒ 1/2 AB = 1/2 BC
(Things which are halves of the same thing are equal to one another)
⇒ AL = MC [From (1) and (2)]

(ii) It is given that L is the mid-point of AB.

∴ AL = BL = 1/2 AB
⇒ 2AL = 2BL = AB .....(3)

As M is the mid-point of BC,

BM = MC = 1/2 BC
⇒ 2BM = 2MC = BC ...(4)

As BL = BM, from equations (3) and (4), AB = BC.