Given, X is the mid-point of AC
AX = CX= ½ AC
⇒ 2AX =2CX = AC …(i)
Y is the mid-point of BC.
BY = CY = ½ BC
⇒ 2BY = 2CY= BC …(ii)
According to the question,
We also have,
AX=CY …(iii)
Applying the Euclid’s axiom,
“Things which are double of the same things are equal to one another”.
We get,
From Eq. (iii),
2AX = 2CY
Using Eqs. (i) and (ii), we get,
AC=BC
Hence Proved.