DAV Class 8 Maths Chapter 10 Worksheet 3 Solutions

The DAV Maths Class 8 Solutions and DAV Class 8 Maths Chapter 10 Worksheet 3 Solutions of Parallel Lines offer comprehensive answers to textbook questions.

DAV Class 8 Maths Ch 10 WS 3 Solutions

Question 1.
Draw a line segment AB = 5 cm and divide it internally into six equal parts.
Answer:
Steps of Construction:
1. Draw a line segment AB = 5 cm.
2. Draw two parallel rays AP and BQ at A and B respectively making an acute angle.
3. Using compass mark equal distance A₁, A₂, A₃, A₄, A₅ and A₆ at AP and B₁, B₂, B₃, B₄, B₅ and B₆ at BQ.

4. Join AB₆, A₁B₅, A₂B₄, A₃B₃, A₄B₂, A₅B₁ and A₆B which cut AB at C₁, C₂, C₃, C₄, C₅ respectively.
5. Measure \(\overline{\mathrm{AC}_1}, \overline{\mathrm{C}_1 \mathrm{C}_2}, \overline{\mathrm{C}_2 \mathrm{C}_3}, \overline{\mathrm{C}_3 \mathrm{C}_4}, \overline{\mathrm{C}_4 \mathrm{C}_5}\) and C₅B which are equal.

Question 2.
Draw a line segment of length 6.4 cm and divide it into four equal parts. What is the length of each part?
Answer:
Steps of Construction:
1. Draw AB = 6.4 cm.
2. Draw rays \(\overrightarrow{\mathrm{AP}} \| \overrightarrow{\mathrm{BQ}}\) at A and B respectively making acute angles with AB .

3. Using compass, mark A₁, A₂, A₃, and B₁, B₂, B₃ on \(\) and \(\) at equal distances.
4. Join AQ, A₁B₃, A₂B₂, A₃B₁ and PB which cut AB at C₁, C₂ and C₃.
5. Measure \(\overline{\mathrm{AC}_1}, \overline{\mathrm{C}_1 \mathrm{C}_2}, \overline{\mathrm{C}_2 \mathrm{C}_3}\), C₃B which are same and length of each part = 1.6 cm.

Question 3.
Draw a line segment of length 5.5 cm. Divide it internally in the ratio 2 : 3. What is the length of each part?
Answer:
Steps of Construction:
1. Draw \(\overline{\mathrm{AB}}\) = 5.5 cm.
2. Draw \(\overrightarrow{\mathrm{AP}} \| \overrightarrow{\mathrm{BQ}}\) at A and B respectively making acute angles.

3. Mark A₁, A₂, A₃, A₄ and B₁, B₂, B₃ and B₄ on \(\overrightarrow{\mathrm{AP}}\) and \(\overrightarrow{\mathrm{BP}}\) respectively at equal distance.
4. Join AQ and BP.
5. Join A₂B₃ which cuts AB at C.
6. C is the required point which divides \(\overrightarrow{\mathrm{AB}}\) in the ratio 2:3.

Question 4.
Draw a line segment of length 6.3 cm and divide it internally in the ratio 3 : 4.
Answer:
Steps of Construction:
1. Draw \(\overline{\mathrm{AB}}\) = 6.3 cm.
2. Draw \(\overrightarrow{\mathrm{AP}} \| \overrightarrow{\mathrm{BQ}}\) at A and B respectively making acute angles with \(\overline{\mathrm{AB}}\) in opposite sides.

3. Mark A₁, A₂, A₃, A₄, A₅, A₆ and B₁, B₂, B₃, B₄, B₅, B₆ on \(\overrightarrow{\mathrm{AP}}\) and \(\overrightarrow{\mathrm{BQ}}\) at equal distances.
4. Join AQ, BP and A₃B₄.
5. A₃B₄ cuts \(\overline{\mathrm{AB}}\) at C which divides \(\overline{\mathrm{AB}}\) in the ratio 3 : 4.

Question 5.
Draw a line segment AB of length 7 cm and find a point P on it such that \(\overline{\mathrm{AP}}: \overline{\mathrm{PB}}\) =1:3. Measure \(\overline{\mathrm{AP}}\) and \(\overline{\mathrm{PB}}\).
Answer:
Steps of Construction:
1. Draw \(\overline{\mathrm{AB}}\) = 7 cm.
2. Draw \(\overline{\mathrm{AP}}: \overline{\mathrm{PB}}\) at A and B respectively making acute angles on the opposite sides of AB.

3. With the help of compass, mark 1 + 3 = 4 points namely A₁, A₂, A₃, A₄ on \(\overrightarrow{\mathrm{AM}}\) and B1; B2, B3, B4 on \(\overrightarrow{\mathrm{AM}}\) at equal distances.
4. Join AB₄ and BA₄.
5. Join A₁ to B₃ which cuts AB at P to divides \(\overrightarrow{\mathrm{AB}}\) in the ratio 1 : 3 i.e. \(\overline{\mathrm{AP}}: \overline{\mathrm{PB}}\) =1:3.

Question 6.
Draw a line segment of a given length. Divide it into four equal parts.
Answer:
Steps of Construction:
1. Draw \(\overline{\mathrm{AB}}\) of any length.
2. Draw \(\overrightarrow{\mathrm{AP}} \| \overrightarrow{\mathrm{BP}}\) at A and B respectively making acute angles on opposite sides of AB.

3. With the help of compass, mark A₁, A₂ A₃ and A₄ on \(\overrightarrow{\mathrm{AP}}\) and B1, B2, B3 and B4 on \(\overrightarrow{\mathrm{BQ}}\) at equal distances.
4. Join AB₄, A₁B₃, A₃B₂, A₃B₁ and A₄B which cut \(\overline{\mathrm{AB}}\) at C₁, C₂ and C₃.
5. Hence, required divisions are
\(\overline{\mathrm{AC}_1}=\overline{\mathrm{C}_1 \mathrm{C}_2}=\overline{\mathrm{C}_2 \mathrm{C}_3}=\overline{\mathrm{C}_3 \mathrm{~B}}\).

Question 7.
Draw a line segment AB = 5.5 cm. Find a point P on it such that \(\overline{\mathrm{AP}}=\frac{2}{3} \overline{\mathrm{BP}}\).
Answer:
Steps of Construction:
1. Draw \(\overline{\mathrm{AB}}\) = 5.5 cm.
2. Draw \(\overrightarrow{\mathrm{AM}} \| \overrightarrow{\mathrm{BN}}\) at A and B respectively making acute angles on the opposite sides of \(\overline{\mathrm{AP}}=3 \overline{\mathrm{BP}}\) .

3. With the help of compass, mark A₁, A₂ A₃, A₄, A₅ on \(\) and B₁, B₂, B₃, B₄, B₅ on \(\) at equal distances.
4. Join AB₅ and BA₅.
5. Join A₂ to B₃ which meets \(\overline{\mathrm{AB}}\) at P such that \(\overline{\mathrm{AP}}: \overline{\mathrm{BP}}\) = 2 : 3 or \(\overline{\mathrm{AP}}=3 \overline{\mathrm{BP}}\).

Question 8.
Draw a line segment AB = 6 cm. Find a point Q on it such that \(\overline{\mathrm{AQ}}=\frac{2}{3} \overline{\mathrm{QB}}\).
Answer:
Steps of Construction:
1. Draw \(\overline{\mathrm{AB}}\) = 6 cm.
2. Draw \(\overrightarrow{\mathrm{AM}} \| \overrightarrow{\mathrm{BN}}\) at A and B respectively making acute angles on the opposite sides of AB.
3. Mark A₁; A₂, A₃, A₄, A₅ on \(\overrightarrow{\mathrm{AM}}\) and B₁; B₂, B₃, B₄ and B₅ on \(\overrightarrow{\mathrm{BN}}\) at equal distances.

4. Join AB₅ and BA₅.
5. Join A₂B₃ which cuts \(\overline{\mathrm{AB}}\) at Q such that \(\overline{\mathrm{AQ}}: \overline{\mathrm{QB}}\) = 2 : 3 i.e. \(\overline{\mathrm{AQ}}=\frac{2}{3} \overline{\mathrm{QB}}\).