According to the question,
We have,
BX = ½ AB and BY = ½ BC
⇒ 2BX = AB ….(i)
⇒ 2BY = BC ….(ii)
It is also given that,
AB = BC …(iii)
Substituting the values from Eqs. (i) and (ii) in eq. (iii), we get,
2BX = 2BY
Applying the Euclid’s axiom, “things which are double of same things are equal to one another”.
BX = BY