Question : In the figure, we have BX=½AB, BY=½BC and AB=BC show that BX=BY. Also write the axiom used.
Doubt by Purvi
Solution :
Given :
BX=½AB
BY=½BC
AB=BC
To Prove : BX=BY
BX=½AB
BY=½BC
AB=BC
To Prove : BX=BY
Proof :
BX=½AB (Given)
2BX=AB
AB=2BX — (1)
2BX=AB
AB=2BX — (1)
BY=½BC (Given)
2BY=BC
BC=2BY — (2)
AB=BC (Given)
2BX=2BY
BX=BY
[Things which are double of the same things are equal to one another]
BC=2BY — (2)
AB=BC (Given)
2BX=2BY
BX=BY
[Things which are double of the same things are equal to one another]
Hence Proved.