Mathematics

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


ANSWER

Things which are equal to the same thing are equal to one another.


SOLUTION
To prove that  $$\triangle ABC$$  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 :
$$Things\ which\ are\ equal\ to\ the\ same\ thing\ are\ equal\ to\ one\ another.\ \ \ \ [C]$$

In other words,
$$A=B\ \ and\ \ B=C\ \Rightarrow\ A=C$$
$$i.e.$$  If we know  $$A=B$$  and  $$B=C$$,  we can say that  $$A+C$$.
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