Q. 54.4( 181 Votes )

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

Answer :

Given to construct an equilateral triangle and justify the construction.

Let us construct an equilateral triangle of 3 cms length on each side.

*Steps of construction*:

i. Draw a ray AX.

ii. With 3 cms as radius, draw an arc with centre as A. The place where the arc meets the ray AZ is point B.

iii. Now, with B as centre, draw another arc with the same 3 cms radius intersecting the previous arc at C.

iv. Now join AC and BC to get the required construction where ΔABC is an equilateral triangle.

*Justification*:

As per the above construction,

*AB = BC* ---- (1)

[*as they are the radii of the same arc*]

Also

*AB = AC* ---- (2)

[*as they are the radii of the same arc*]

From (1) & (2), we have *AB = BC= AC*

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