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 A_{1}, A_{2}, A_{3}, A_{4}, A_{5} and A_{6} at AP and B_{1}, B_{2}, B_{3}, B_{4}, B_{5} and B_{6} at BQ.

4. Join AB_{6}, A_{1}B_{5}, A_{2}B_{4}, A_{3}B_{3}, A_{4}B_{2}, A_{5}B_{1} and A_{6}B which cut AB at C_{1}, C_{2}, C_{3}, C_{4}, C_{5} 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 C_{5}B 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 A_{1}, A_{2}, A_{3}, and B_{1}, B_{2}, B_{3} on \(\) and \(\) at equal distances.

4. Join AQ, A_{1}B_{3}, A_{2}B_{2}, A_{3}B_{1} and PB which cut AB at C_{1}, C_{2} and C_{3}.

5. Measure \(\overline{\mathrm{AC}_1}, \overline{\mathrm{C}_1 \mathrm{C}_2}, \overline{\mathrm{C}_2 \mathrm{C}_3}\), C_{3}B 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 A_{1}, A_{2}, A_{3}, A_{4} and B_{1}, B_{2}, B_{3} and B_{4} on \(\overrightarrow{\mathrm{AP}}\) and \(\overrightarrow{\mathrm{BP}}\) respectively at equal distance.

4. Join AQ and BP.

5. Join A_{2}B_{3} 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 A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6} and B_{1}, B_{2}, B_{3}, B_{4}, B_{5}, B_{6} on \(\overrightarrow{\mathrm{AP}}\) and \(\overrightarrow{\mathrm{BQ}}\) at equal distances.

4. Join AQ, BP and A_{3}B_{4}.

5. A_{3}B_{4} 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 A_{1}, A_{2}, A_{3}, A_{4} on \(\overrightarrow{\mathrm{AM}}\) and B1; B2, B3, B4 on \(\overrightarrow{\mathrm{AM}}\) at equal distances.

4. Join AB_{4} and BA_{4}.

5. Join A_{1} to B_{3} 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 A_{1}, A_{2} A_{3} and A_{4} on \(\overrightarrow{\mathrm{AP}}\) and B1, B2, B3 and B4 on \(\overrightarrow{\mathrm{BQ}}\) at equal distances.

4. Join AB_{4}, A_{1}B_{3}, A_{3}B_{2}, A_{3}B_{1} and A_{4}B which cut \(\overline{\mathrm{AB}}\) at C_{1}, C_{2} and C_{3}.

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 A_{1}, A_{2} A_{3}, A_{4}, A_{5} on \(\) and B_{1}, B_{2}, B_{3}, B_{4}, B_{5} on \(\) at equal distances.

4. Join AB_{5} and BA_{5}.

5. Join A_{2} to B_{3} 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 A_{1}; A_{2}, A_{3}, A_{4}, A_{5} on \(\overrightarrow{\mathrm{AM}}\) and B_{1}; B_{2}, B_{3}, B_{4} and B_{5} on \(\overrightarrow{\mathrm{BN}}\) at equal distances.

4. Join AB_{5} and BA_{5}.

5. Join A_{2}B_{3} which cuts \(\overline{\mathrm{AB}}\) at Q such that \(\overline{\mathrm{AQ}}: \overline{\mathrm{QB}}\) = 2 : 3 i.e. \(\overline{\mathrm{AQ}}=\frac{2}{3} \overline{\mathrm{QB}}\).