These NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.2

Question 1.

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

Answer:

Steps of construction:

- Place the zero mark of the ruler at a point A.
- Mark a point B at a distance of 7.3 cm from A.
- Join AB.

Hence, \(\overline{\mathrm{AB}}\) is the required line segment of length 7.3 cm.

Question 2.

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

Answer:

Steps of construction:

- Draw a line ’l’. 1 Mark a point A on this line.
- Place the compasses pointer on zero mark of the ruler. Open it to place the pencil point up to 5.6 cm mark.
- Without changing the opening of the compasses. Place the pointer on A and cut an arc ’l’ at B.

\(\overline{\mathrm{AB}}\) is the required line segment of length 5.6 cm.

Question 3.

Construct \(\overline{\mathrm{AB}}\) of length 7.8 cm. From this, cut off \(\overline{\mathrm{AC}}\) of length 4.7 cm. Measure \(\overline{\mathrm{BC}}\).

Answer:

Steps of construction:

- Place the zero mark of the ruler at A.
- Mark a point B at a distance 7.8 cm from A.
- Again, mark a point C at a distance 4.7 from A.

Hence, by measuring \(\overline{\mathrm{BC}}\), we find that BC = 3.1 cm.

Question 4.

Given \(\overline{\mathrm{AB}}\) of length 3.9 cm, construct \(\overline{\mathrm{PQ}}\) such that the length of \(\overline{\mathrm{PQ}}\) is twice that of \(\overline{\mathrm{AB}}\). Verify by measurement.

(Hint: construct \(\overline{\mathrm{PX}}\) such that length of \(\overline{\mathrm{PX}}\) = length of \(\overline{\mathrm{AB}}\); then cut off \(\overline{\mathrm{XQ}}\) such that \(\overline{\mathrm{XQ}}\) also has the length of \(\overline{\mathrm{AB}}\).)

Answer:

Steps of construction:

- Draw a line ’l’.
- Construct \(\overline{\mathrm{PX}}\) such that length of \(\overline{\mathrm{PX}}\) = length of \(\overline{\mathrm{AB}}\)
- Then cut of \(\overline{\mathrm{XQ}}\) such that \(\overline{\mathrm{XQ}}\) also has the length of \(\overline{\mathrm{AB}}\).

- Thus the length of \(\overline{\mathrm{PX}}\) and the length of \(\overline{\mathrm{XQ}}\) added together make twice the length of \(\overline{\mathrm{AB}}\)

Verification:

Hence, by measurement we find that PQ = 7.8 cm = 3.9 cm + 3.9 cm =

\(\overline{\mathrm{AB}}+\overline{\mathrm{AB}}\) 2 × \(\overline{\mathrm{AB}}\)

Question 5.

Given AB of length 7.3 cm and \(\overline{\mathrm{CD}}\) of length 3.4 cm, construct a line segment \(\overline{\mathrm{XY}}\) such that the length of \(\overline{\mathrm{XY}}\) is equal to the difference between the lengths of \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\) Verify by measurement.

Answer:

Steps of construction:

- Draw a line ‘l’ and take a point X on it.
- Construct \(\overline{\mathrm{XZ}}\) such that length \(\overline{\mathrm{XZ}}\) = length of \(\overline{\mathrm{AB}}\) = 7.3 cm
- Then cut off \(\overline{\mathrm{ZY}}\) = length of \(\overline{\mathrm{CD}}\) = 3.4 cm
- Thus the length of \(\overline{\mathrm{XY}}\) = length of \(\overline{\mathrm{AB}}\) – length of \(\overline{\mathrm{CD}}\)

Verification:

Hence, by measurement we find that length of \(\overline{\mathrm{XY}}\) = 3.9 cm = 73. cm -3.4 cm = \(\overline{\mathrm{AB}}-\overline{\mathrm{CD}}\)