Q5.    Construct an equilateral triangle, given its side and justify the construction.

The following steps to make an equilateral triangle:

Step 1: Draw a line segment AB = 4 cm.

Step 2: With A and B as centres, make two arcs in the line segment AB. Mark it as D and E respectively.

Step 3: Now, with D and E as centres, make the two arcs cutting the previous arcs respectively, and forming an angle of $60^{\circ }$ each.

Step 4: Extend the lines of A and B until they intersect each other at point C.

Hence, triangle constructed is ABC which is equilateral.

Now, Justification;

Since the angles constructed are of $60^{\circ }$ each, so the third angle will also be $60^{\circ }$.

$\left [ \because The\ sum\ of\ all\ angles\ of\ triangle = 180^{\circ} \right ]$

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