CBSE Class 6 Mathematics Practical Geometry Assignment Set 04

VI - Mathematics Assignment No-02 - Practical Geometry

Q1. Draw a line segment of length \(6.4\text{ cm}\) using ruler.
Answer: Steps of construction:
1. Mark a point \(A\) on a paper.
2. Place the zero mark of the ruler adjacent to point \(A\).
3. Move along the edge of the ruler up to \(6.4\text{ cm}\) and mark a point \(B\).
4. Join points \(A\) and \(B\). Thus, \(AB\) is the required line segment of length \(6.4\text{ cm}\).
In simple words: Use a ruler to measure and draw a straight line of exactly \(6.4\text{ cm}\).

Exam Tip: Ensure the ruler is held firmly and your eye is directly above the markings to avoid parallax error.

Q2. Cut a length of \(3.2\text{ cm}\) from a line segment of length \(9\text{ cm}\). Find the measurement of the remaining length.
Answer: Total length of the line segment = \(9\text{ cm}\)
Length to be cut = \(3.2\text{ cm}\)
Remaining length = \(9\text{ cm} - 3.2\text{ cm} = 5.8\text{ cm}\)
In simple words: Subtract the cut length from the total length using simple subtraction.

Exam Tip: Always align the decimal points properly when subtracting decimals.

Q3. Given a line segment of length \(7.8\text{ cm}\) and another line segment of length \(2.2\text{ cm}\). Find the measurement of the sum of these two lengths.
Answer: Length of the first line segment = \(7.8\text{ cm}\)
Length of the second line segment = \(2.2\text{ cm}\)
Sum of the two lengths = \(7.8\text{ cm} + 2.2\text{ cm} = 10.0\text{ cm}\) (or \(10\text{ cm}\))
In simple words: Add both lengths together to get the total length.

Exam Tip: Include units (\(\text{cm}\)) in your final answer.

Q4. Given a length \(AB\) of \(8.4\text{ cm}\) and another length \(CD\) of \(3.2\text{ cm}\). Construct a length of (i) \(AB + CD\) (ii) \(AB - CD\) (iii) \(2AB\) (iv) \(AB - 2CD\)
Answer: Given: \(AB = 8.4\text{ cm}\), \(CD = 3.2\text{ cm}\)
(i) \(AB + CD = 8.4\text{ cm} + 3.2\text{ cm} = 11.6\text{ cm}\)
(ii) \(AB - CD = 8.4\text{ cm} - 3.2\text{ cm} = 5.2\text{ cm}\)
(iii) \(2AB = 2 \times 8.4\text{ cm} = 16.8\text{ cm}\)
(iv) \(AB - 2CD = 8.4\text{ cm} - (2 \times 3.2\text{ cm}) = 8.4\text{ cm} - 6.4\text{ cm} = 2.0\text{ cm}\)
In simple words: Perform standard arithmetic operations on the given lengths to find the required measurements.

Exam Tip: Follow the order of operations, especially when multiplication and subtraction are combined in part (iv).

Q5. Given a length \(AB\) of \(3.2\text{ cm}\). Construct another length which is half of \(AB\)
Answer: Length of \(AB = 3.2\text{ cm}\)
Required length = \(\frac{1}{2} \times AB = \frac{3.2\text{ cm}}{2} = 1.6\text{ cm}\)
Steps of construction: Draw a line segment \(AB = 3.2\text{ cm}\). Using a ruler or perpendicular bisector construction, locate the midpoint such that the required segment measures \(1.6\text{ cm}\).
In simple words: Divide the length by 2 to find half of the given measurement.

Exam Tip: Division by 2 gives the exact midpoint value for linear segments.

Q6. Draw a line segment \(AB = 5\text{ cm}\). Find a point \(M\) on it such that \(M\) divides \(AB\) into two equal parts using ruler and compass only.
Answer: Steps of construction:
1. Draw a line segment \(AB = 5\text{ cm}\) using a ruler.
2. With \(A\) as center and radius more than half of \(AB\), draw arcs above and below the line segment \(AB$.
3. With \(B\) as center and the same radius, draw arcs cutting the previous arcs at points \(P\) and \(Q$.
4. Join \(PQ\) intersecting \(AB\) at point \(M\).
5. Point \(M\) is the required midpoint dividing \(AB\) into two equal parts (\(AM = MB = 2.5\text{ cm}\)).
In simple words: Draw perpendicular bisector using a compass to find the exact middle point.

Exam Tip: Do not change the compass width while drawing intersecting arcs from both endpoints.

Q7. Take a line segment \(AB = 6.2\text{ cm}\). Take a point \(P\) outside \(AB\). From \(P\), draw a perpendicular on \(AB\)
Answer: Steps of construction:
1. Draw a line segment \(AB = 6.2\text{ cm}\).
2. Take a point \(P\) outside the line segment \(AB\).
3. With \(P\) as center, draw an arc of convenient radius that intersects \(AB\) at two distinct points, say \(C\) and \(D\).
4. With \(C\) and \(D\) as centers and radius greater than half of \(CD\), draw two arcs on the other side of \(AB\) intersecting each other at \(Q\).
5. Join \(PQ\). Then \(PQ\) is perpendicular to \(AB\).
In simple words: Drop a straight \(90\)-degree line from an outside point onto the line segment.

Q8. Draw any line of any length. Take a point \(P\) on the line. From this point, draw a line segment \(PQ\) perpendicular to the line
Answer: Steps of construction:
1. Draw a line \(l\).
2. Mark a point \(P\) on line \(l\).
3. With \(P\) as center and a convenient radius, draw an arc intersecting line \(l\) at two points \(A\) and \(B\).
4. With \(A\) and \(B\) as centers and radius greater than \(AP\), draw two arcs above (or below) point \(P\) which intersect each other at \(Q\).
5. Join \(PQ\). Thus, \(PQ \perp l\).
In simple words: Construct a right angle directly upward from a chosen point on a line.

Exam Tip: Use the standard semicircle arc method with a compass for accuracy.

Q9. Draw a line of \(10\text{ cm}\) length. Divide it into four equal parts and measure each part. Also verify this part by actual calculations.
Answer: Given total length = \(10\text{ cm}\)
Number of parts = \(4$
Measured length of each part using ruler = \(2.5\text{ cm}\)
Verification by calculation:
Length of each part = \( \frac{10\text{ cm}}{4} = 2.5\text{ cm} $
In simple words: Divide the total length by 4 to get four equal segments of \(2.5\text{ cm}\) each.

Exam Tip: You can divide a line into four parts by bisecting the line first, and then bisecting each of the two halves.

Q10. Draw the perpendicular bisector of a line segment \(AB\) of \(10.4\text{ cm}\). Take a point \(P\) on this perpendicular bisector and verify that \(PA = PB\)
Answer: Steps of construction:
1. Draw a line segment \(AB = 10.4\text{ cm}\).
2. Draw its perpendicular bisector using a compass (arcs from \(A\) and \(B\) intersecting above and below).
3. Choose any point \(P\) on this perpendicular bisector line.
4. Measure the lengths of \(PA\) and \(PB\) using a ruler.
5. Verification: Both lengths will be found equal (\(PA = PB = 5.9\text{ cm}\) approximately, depending on the chosen height of \(P\)).
In simple words: Any point on the perpendicular bisector of a line segment is equidistant from both endpoints.

Exam Tip: This fundamental property states that points on a perpendicular bisector are always equidistant from the endpoints.