Question

In fig, point C is called a midpoint of line segment AB. Prove that every line segment has one and only one mid-point.

Answer 1

Let C and D are two points **** on AB.

C is the mid-point of AB.

AC = BC

Adding AC on both sides,

AC + AC = BC + AC

2AC = AB → (i)

D is the mid-point of AB,

AD = DB

Adding AD on both sides,

AD + AD = DB + AD

2AD = AB → (ii)

From equations (i) and (ii),

2AC = 2 AD.

∴ AC = AD.

Then C and D are not different, they are same.

∴ “Every segment has one and only one mid-point.”