Question

Draw a random line segment and then trisect it?

Answer 1

See below.

Explanation:

In one extremity of the random line segment, along a line slanted and passing by this extremity, draw three equal length segments. Then, using the Thales of Miletus theorem,

https://en.wikipedia.org/wiki/Thales

you can divide the random segment into three equal subsegments.

Answer 2

STEPS FOLLOWED

• A random line segment is first drawn by a ruler and a pencil.

• Two equal alternate interior angles `/_XAB and /_YBA` of suitable measure are drawn at A and B respectively with the help of a ruler and a pencil compass .

• Two line segments `(AP and PQ)` of same suitable length are cut off from AB by a pencil compass.

• Another two line segments `(BR and RS)` of same suitable length as `AP and PQ` are also cut off from AB by a pencil compass.

• Finally `P,S and Q,R` are joined with the help of a ruler and a
  pencil.

`PS and QR` intersect `AB" at "C and D` respectively.

As a result the line segment AB is trisected at C and D. The equality of length of three line segments AC,CD and DB is verified with the help of a divider.