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Answer :

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.

- Construct an angle of \(90^\circ\) at the initial point of a given ray and justify the construction.
- Construct an angle of \(45^\circ\) at the initial point of a given ray and justify the construction.
- Construct the angles of the following measurements:I)\(30^\circ\)II) \(22\frac{1}{2} )^\circ\)III)\(15^\circ\)
- Construct the following angles and verify by measuring then by a protractor: I)\(75^\circ\)II) \(105^\circ\)III)\(135^\circ\)

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