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

Steps of construction:


1. Take a ray AX with initial point A. From AX, cut off AB = 4cm.

2. Taking A as centre and radius (= 4 cm), draw an arc of a circle, which intersects AX, say at a point B.

3. Taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc, say at a point C.

4. Draw the ray AE passing through C.

5. Next, taking B as centre and radius (= 4 cm), draw an arc of a circle, which intersects AX, say at a point A.

6. Taking A as centre and with the same radius as in step 5, draw an arc intersecting the previously drawn arc, say at a point C.

7. Draw the ray BF passing through C. Then, ABC is the required triangle with gives side 4 cm.


Justification:
AB = BC ...(By construction)
AB = AC ...(By construction)
Thus, AB = BC = CA
Therefore, \(\triangle{ABC}\) is an equilateral triangle.
Hence, The construction is justified.