Question

In the figure,A and B are the centres of the two intersecting circles.Which Euclid's axiom will prove that the $△ABC$ is an equilateral triangles?

• A. If equals are added to equals,the wholes are equal.
• B. Things which are double of the same things are equal to one another.
• C. Things which are equal to the same thing are equal to one another.
• D. If equals are subtracted from equals,the remainders are equal.

Answer 1

The correct option is C Things which are equal to the same thing are equal to one another.

To prove that $△ABC$ is equilateral, either we have to prove $AB=BC=CA$ or $\angle A=\angle B=\angle C$.

Here in this case, we need to prove $\angle A=\angle B=\angle C$.

If we have to prove three things are equal, we use the Euclid's axiom stated below :

$Thingswhichareequaltothesamethingareequaltooneanother.\left[C\right]$

In other words,

$A=BandB=C\Rightarrow A=C$

$i.e.$ If we know $A=B$ and $B=C$, we can say that $A+C$.