Question

The things which are double of same thing are :
A. Equal
B. Halves of same thing
C. Unequal
D. Double of the same thing

Answer 1

Hint: In this question, we are not given any value or equation but we can write an equation on our own by taking any two variables and considering their doubles to be equal. According to Euclid's axiom, "Things which are double of the same thing are equal ", we can see that the correct answer is equal. Although, we can see it is true by the axiom itself and we can directly write it but it is always better to write the proof of the axiom while we solve these problems related to the axiom.

Complete step by step solution :
Let us take two variables , say $x$ and $y$
Now let us take the double of $x$ and $y$ and equate them
Then we get
\[2x=2y\]
Since \[2!=0\]
So we can divide both RHS and LHS by \[2\]
On dividing , we get
\[x=y\]
Thus both of them are equal

Hence, A is the correct option.

Note :
We can also prove this using another method. In this method, we will take three variables a, b and x such that a and b are equal to twice of $x$. This implies \[a=2x\] and \[b=2x\]. Then according to Euclid's axiom which states if first number is equal to second which is equal to third then first is equal to third. So, we get \[a=b\].