Question

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

Answer 1

$<b><i>$
$<u>Answer :</u>$

Given,

AB = BC … (i)

And BX = 1/2 AB and BY = 1/2 BC … (ii)

By Euclid’s axiom 7,

$<u>We know that things which are halves of the same thing are equal to one another.</u>$

From (i) and (ii),

∴ BX = BY

Answer 2

Answer:

BX=BY ....Proved.

Step-by-step explanation:

In the given figure, we have a triangle ABC, whose sides AB=BC ........ (1)

So, the triangle can be said to be an isosceles triangle.

Now, X and Y are two points on the sides AB and BC respectively, in such a way that, length BX=1/2 of legth AB, ⇒BX=AB/2, ⇒AB=2×BX ...... (2)

And length BY =1/2 of length BC, ⇒ BY=BC/2, ⇒BC =2×BY .......(3)

Hence, from the relations (1), (2), and (3), we can write,

2×BX =2×BY, ⇒ BX=BY (Proved)