Question

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

Answer 1

Let the equilateral triangle be $ABC$

$1.$Draw $AB=5$cm

$2.$Taking $A$ and $B$ as centers, radius $=AB=5$cm,draw two arcs intersecting each other at $A$

$3.$Join $AB$ and $AC$

Thus, $△ABC$ is our required triangle.

Justification:

By construction,$AB=AC=BC$(radius of equal arcs)

Since all sides are equal.

$\therefore △ABC$ is an equilateral triangle.

Thus, the construction is justified