**Practical Geometry**

**Question 1.Draw a line segment of length 7.3 cm, using a ruler.**

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

- Mark a point A on the plane of the paper and place the ruler so that zero mark of the ruler is at A.

- Mark with pencil a point B against the mark on the ruler which indicates 7.3 cm.
- Join points A and B by moving the tip of the pencil against the straight edge of the ruler.

The line segment AB so obtained is the required line segment.

**Question 2.Construct a line segment of length 5.6 cm using ruler and compasses.**

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

- Mark a point A on the plane of the paper and draw a line, say l, passing through it.
- Place the steel end of the compasses at zero mark on the ruler and open out it such that the pencil end on the mark indicates 5.6 cm.
- Transfer the compasses as it is to the line l so that the steel end is on A.
- With the pencil end make a small stroke on l so as to cut it at B.
- The segment AB so obtained is the required line segment.

**Question 3.Construct of length 7.8 cm. From this, cut off of length 4.7 cm. Measure .**

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

- Draw a line segment AB of length 7.8 cm.
- Using compasses find a point C on the line segment AB so that segment AC = 4.7 cm.
- On measuring BC, we find that BC = 3.1 cm.

**Question 4.Given of length 3.9 cm, construct such that the length of is twice that of . Verify by measurement.**

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

- Draw a line l and mark a point P on it.
- Using compasses find a point X so that PX(= AB) = 3.9 cm on the line l.
- Using compasses find a point Q so that XQ = 3.9 cm on the line l.

Thus, PQ = PX + XQ = 3.9 cm + 3.9 cm

= 2(3.9 cm) = 2AB.

**Question 5.Given of length 7.3 cm and of length 3.4 cm, construct a line segment such that the length of is equal to the difference between the lengths of and . Verify by measurement**

**Solution:**

**Steps of Construction:**- Draw line segments AB = 7.3 cm and CD = 3.4 cm.
- Draw a line l and mark a point X on it.
- Using compasses find a point P on the line l so that segment XP = segment AB (i.e., 7.3 cm).
- Using compasses find a point Y so that the segment PY = segment CD (i.e., 3.4 cm). The segment XY so obtained is the required segment, because XY = OP -PY – AB -CD.