GSEB Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.2

Gujarat Board 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 ‘A’ 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 ‘A’ and mark an arc to cut l at ‘B’.
Thus, $\overline{A B}$ = 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 $\overline{A C}$ = 4.7 cm.
Step IV: Measure the line segment $\overline{B C}$. We find that $\overline{B C}$ =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 $\overline{P X}$ = $\overline{A B}$ (= 3.9 cm).
Step IV: Next construct $\overline{X Q}$ = $\overline{A B}$ (=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:
$\overline{A B}$ + $\overline{A B}$ = 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 $\overline{C D}$ Verify by measurement.
Solution:
Step I: Draw $\overline{A B}$ = 7.3 cm and $\overline{C D}$ =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 $\overline{A B}$ (= 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, $\overline{C D}$ is a copy of $\overline{A B}$.