Medium
Solve the following question using the appropriate Euclid's axiom:
In the figure,we have
$\angle 1 = \angle 3$ and $\angle 2 = \angle 4$. Show that $\angle A = \angle C$.
In the figure,we have
$\angle 1 = \angle 3$ and $\angle 2 = \angle 4$. Show that $\angle A = \angle C$.
(N/A) We have $\angle 1 = \angle 3$ ..... $(1)$ [Given]
And $\angle 2 = \angle 4$ ..... $(2)$ [Given]
Now,by Euclid's axiom $2$,which states that if equals are added to equals,the wholes are equal.
Adding $(1)$ and $(2)$,we get
$\angle 1 + \angle 2 = \angle 3 + \angle 4$
Since $\angle 1 + \angle 2 = \angle A$ and $\angle 3 + \angle 4 = \angle C$,
Therefore,$\angle A = \angle C$.
And $\angle 2 = \angle 4$ ..... $(2)$ [Given]
Now,by Euclid's axiom $2$,which states that if equals are added to equals,the wholes are equal.
Adding $(1)$ and $(2)$,we get
$\angle 1 + \angle 2 = \angle 3 + \angle 4$
Since $\angle 1 + \angle 2 = \angle A$ and $\angle 3 + \angle 4 = \angle C$,
Therefore,$\angle A = \angle C$.
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