**Practical Geometry**

**Question 1.Draw any line segment . Without measuring , construct a copy of .**

**Solution:***Steps of Construction:*

Let PQ be the given line segment and l be a given line.

- Mark a point 0 on the line l.
- Open out the compasses and adjust so that the steel end is on A and the pencil end is A on B.
- Transfer the compasses to the line l without disturbing their opening so that the steel end is on 0.
- With the pencil end make a small stroke on the line l to cut it at the point P.

Then, the fine segment OP so obtained = the given line segment AB.

**Question 2.Given some line segment , whose length you do not know, construct such that the length of is twice that of .**

**Solution:**

**Steps of Construction:**Let AB be the given line segment.Draw any line l and make a point 0 on it.

- Open out the compasses in such way that the steel end is on A and the pencil end is on B.
- Transfer the compasses without disturbing their opening to the line l so that the steel end is on O.
- With the pencil end make a small stroke on -the line l to cut it at the point P.
- Repeat the steps 3 and 4 with same opening having P as the initial point and Q as the terminal point.

Then, the segment OQ = OP + PQ = AB + AB= 2 AB.