If AB is a line and C is the mid-point of AB and D is mid-point of AC then prove that .

Given: AB is a line.

C is the mid-point of the line AB.

D is the mid-point of AC.

To Prove

Proof: By Euclid’s axiom, we have

‘Things which are halves of the same things are equal to one another’.

Note, given that C is the mid-point of AB.

⇒ AC = CB …(i)

But, AB = AC + CB

⇒ AB = AC + AC [from the equation (i)]

⇒ AB = 2 AC

…(ii)

Also, given that D is the mid-point of AC.

⇒ AD = DC …(iii)

But, AC = AD + DC

⇒ AC = AD + AD [from the equation (iii)]

⇒ AC = 2 AD

…(iv)

Now, put the value of AC from equation (ii) to the equation (iv), we get

Thus, proved.