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# Construct an equilateral triangle, given its side and justify the construction.

To do:

We have to construct an equilateral triangle, given its side and justify the construction

Solution:

__Steps of construction:__

(i) Let us draw a line segment $BC$ of length $5\ cm$.

(ii) Cut an arc of radius $5\ cm$ from point $B$ and an arc of $5\ cm$ from point $C$.

(iii) Name the point of intersection of arcs as point $A$.

(iv) Now, join $AC$ and $BC$. $\Delta ABC$ is the required triangle.

Justification:

From $\Delta ABC$ we have,

$BC= 5\ cm$, $\angle B=60^o$ and $\angle C=60^o$

We know that

The sum of the interior angles of a triangle is always equal to $180^o$

$\angle A+\angle B+\angle C = 180^o$

This implies,

$\angle A+60^o+60^o=180^o$

$\angle A+ 120^o=180^o$

$\angle A=60^o$

We know that,

The sides opposite to equal angles are equal

Therefore, we get,

$CA=AB=5\ cm$

We have,

$BC=CA=AB=5\ cm$ and

$\angle A=\angle B=\angle C=60^o$

Therefore, justified.

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