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}).