In the adjoining figure , if `BX=(1)/(2)AB,BY=(1)/(2)BCand AB=BC`, then show that BX =BY.

Explanation

Given , `BX=(1)/(2)ABrArr2BX=AB` ...(i)
`BY=(1)/(2)BC`
`rArr` 2BY=BC ...(ii)
and AB=BC ...(iii)
On putting the values from Eqs. (i) and (ii) in Eq. (iii) , we get
2BX=2BY
According to Euclid's axiom, things which are double of the same things are equal to one another.
`:.` BX=BY