1.

In the adjoining figure, if BX = ½ AB, BY = ½ BC and AB = BC, then show that BX = BY.

Answer»

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



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