An equilateral triangle can be constructed geometrically by using geometric tools. It is actually constructed by drawing sides of triangle with same length. The following animated example teaches you the geometrical procedure to construct an equilateral triangle.
Let’s investigate the basic properties of equilateral triangle from this constructed triangle.
It is taken that the length of the side $\overline{MN}$ is $10 \, cm$ and also drawn arcs from points $M$ and $N$ with the same length.
Therefore, $MN = NO = OM$ $\,=\,$ $10 \, cm$
Measure all three angles of this equilateral triangle by protractor. You will observe that,
$(1) \,\,\,$ $\angle MNO = 60^°$
$(2) \,\,\,$ $\angle NOM = 60^°$
$(3) \,\,\,$ $\angle OMN = 60^°$
It clears that all three angles of this triangle are equal and each angle is $\dfrac{\pi}{3}$. Therefore, it is proved that an equilateral triangle is also an equiangular triangle.
$\,\,\, \therefore \,\,\,\,\,\,$ $\angle MNO$ $\,=\,$ $\angle NOM$ $\,=\,$ $\angle OMN$ $\,=\,$ $60^°$
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