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

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

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The following steps to make an equilateral triangle:

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

line segment AB

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

cut line segment AB

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.

triangle ABC

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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