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Construct an equilateral triangle, given its side and justify the construction.
We have to construct an equilateral triangle, given its side and justify the construction
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.
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 $180^o$
$\angle A+\angle B+\angle C = 180^o$
$\angle A+ 120^o=180^o$
We know that,
The sides opposite to equal angles are equal
Therefore, we get,
$BC=CA=AB=5\ cm$ and
$\angle A=\angle B=\angle C=60^o$
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