Answer :

Given: Length of a line segment = 9cm

Steps of Construction

Step1: Draw a line segment AB = 9cm

Step 2: From point A, draw a line segment at any angle.

Step 3: Now, take the compass and keep the needle on point A, and set its width to a bit less than one third of the length of AX and mark the three arcs of same length.

Step 4: Label the last arc C.

Step 5: Take the compass and keep the needle on point C and take the width CB, draw an arc from A just below it.

Step 6: Now, set the width of AC in compass, draw an arc from B intersecting the arc drawn in step 5. This intersection point is D. Join D to B

Step 7: Using the same compass width as used in step 3 along AC, step the compass from D along DB and make 3 arcs across the line.

Step 8: Join C to B and draw the lines between the corresponding points along AC and DB.

Hence, the lines divide the given line segment into 3 equal parts and each part is of 3cm

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