Gujarat BoardĀ GSEB Textbook Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.2

Question 1.

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

Solution:

Steps of construction:

Step I: Mark a point A.

Step II: Place the zero mark of the ruler against point A.

Step III: Mark a point B at a distance of 7.3 cm from A.

Step IV: Join A and B.

Thus, \(\overline{A B}\) is the required line segment of length 7.3 cm.

Note: While marking points A and B, we should look straight down at the measuring device. Otherwise, we will get the incorrect length.

Question 2.

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

Solution:

Steps of construction:

Step I: Draw a line l and mark a point āAā on it.

Step II: Place the steel-end of the compasses on the zero mark of the ruler. Open it such that the pencil tip falls on the 5.6 cm mark.

Step III: Without changing the opening of the compasses, place the steel end on āAā and mark an arc to cut l at āBā.

Thus, \(\overline{A B}\)Ā = 5.6 cm is the line segment of the required length.

Question 3.

Construct \(\overline{A B}\) of length 7.8 cm. From this, cut-off \(\overline{A C}\) of length 4.7 cm. Measure \(\overline{B C}\)

Solution:

Steps of construction:

Step I: Place the zero mark of the ruler at A.

Step II: Mark a point B at a distance of 7.8 cm from A.

Step III: Mark another point C between A and B at a distance of 4.7 cm from A such that \(\overline{A C}\)Ā = 4.7 cm.

Step IV: Measure the line segment \(\overline{B C}\). We find that \(\overline{B C}\)Ā =3.1 cm.

Question 4.

Given \(\overline{A B}\) of length 3.9 cm, construct \(\overline{P Q}\) such that the length of \(\overline{P Q}\) is twice that of \(\overline{A B}\). Verify by measurement.

Hint: Construct \(\overline{P X}\) such that length of \(\overline{P X}\) = length of \(\overline{A B}\); then cut-off \(\overline{X Q}\) such that \(\overline{X Q}\) also has the length of \(\overline{A B}\).

Solution:

Steps of construction:

Step I: Draw a line l.

Step II: Draw AB = 3.9 cm.

Step III: On line l construct \(\overline{P X}\) = \(\overline{A B}\)Ā (= 3.9 cm).

Step IV: Next construct \(\overline{X Q}\) = \(\overline{A B}\)Ā (=3.9 cm)

Thus, the lengths of \(\overline{P X}\) and \(\overline{X Q}\) are added together to make twice the length of \(\overline{A B}\)

Verification: By measurement, we have:

\(\overline{A B}\) + \(\overline{A B}\)Ā = 3.9 cm + 3.9 cm

2 ( \(\overline{A B}\) ) = 7.8 cm = \(\overline{X Y}\)

Thus, twice of \(\overline{A B}\) is equal to \(\overline{X Y}\)

Question 5.

Given length 7.3 cm and \(\overline{C D}\) of length 3.4 cm, construct a line segment \(\overline{X Y}\) such that the length of \(\overline{X Y}\) is equal to the difference between the lengths of \(\overline{A B}\) and \(\overline{C D}\)Ā Verify by measurement.

Solution:

Step I: Draw \(\overline{A B}\) = 7.3 cm and \(\overline{C D}\)Ā =3.4 cm.

Step II: Draw a line l and take a point X on it.

Step III: Construct \(\overline{X R}\) such that length of \(\overline{X R}\) = length \(\overline{A B}\)Ā (= 7.3 cm).

Step IV: Cut-off \(\overline{RY}\) = length of \(\overline{C D}\) (= 3.4 cm) such that the length \(\overline{X Y}\) = length

of \(\overline{A B}\) – length of \(\overline{C D}\).

Verification: By measurement, we have

\(\overline{X Y}\) = 3.9 cm = 7.3 cm – 3.4 cm

= \(\overline{A B}\) – \(\overline{C D}\)

Thus, we get \(\overline{X Y}\) = \(\overline{A B}\) – \(\overline{C D}\)

Now, the opening of compasses is equal to \(\overline{A B}\).

Step IV: Draw a line l and mark a point C on it.

Step V: Without changing the openings of the compasses, place the steel end at C and mark a point D on l.

Now, \(\overline{C D}\)Ā is a copy of \(\overline{A B}\).