In the Fig.5.6, we have BX = 1/2 AB and BY = 1/2 BC and AB = BC. Show that BX = BY.

*Note: Thinking process should be, things which are double of the same things are equal to one another.

Given, BX = and BY =

⇒ 2BX = AB ….(i)

⇒ 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 same things are equal to one another.

BX =BY