CBSE Class 6 Mathematics Shapes Assignment Set 08

Question 1. From the following, find which is greater segment and by how much.
Answer: By measuring with a ruler, we find the lengths of the two line segments:
Length of segment AB = 3.5 cm
Length of segment CD = 4 cm
Comparing the two, segment CD is longer.
Difference = CD - AB = 4 cm - 3.5 cm = 0.5 cm
So, segment CD is longer than segment AB by 0.5 cm.
In simple words: When we measure both lines, CD is longer. It is 0.5 cm longer than AB.

Exam Tip: Always use a sharp pencil and a transparent ruler to get exact measurements of line segments.

Question 2. Draw 5 line segments of size 3 cm, 3.2 cm, 5.1 cm, 6.2 cm and 7.3 cm.
Answer: Here are the steps to draw any line segment:
1. Put a ruler down on your paper.
2. Mark a point at 0 on the ruler. This is the start of your line.
3. Mark another point at the required length (like 3 cm) on the ruler.
4. Draw a straight line between these two points with a pencil.
Following these steps, we can draw all five segments:
In simple words: Use a ruler to mark the start at 0 and the end at the given number. Connect them with a straight line.

Exam Tip: Keep your pencil very sharp so your marks on the paper are very precise.

Question 3. In the above figure, name
(i) any 4 line segments
(ii) any 3 rays
Answer:
(i) Four line segments from this drawing are: \( \text{EG} \), \( \text{EF} \), \( \text{GH} \), and \( \text{CE} \).
(ii) Three rays shown in this drawing are: ray \( \text{EC} \), ray \( \text{FD} \), and ray \( \text{GA} \).
In simple words: Line segments have two endpoints. Rays have one starting point and go on forever in one direction.

Exam Tip: When naming a ray, always write the starting point first, then any other point along the ray's direction.

Question 4. Given three non-collinear points, how many line segments can be formed name them.
Answer: Non-collinear points are points that are not on the same straight line. Let's call these three points A, B, and C.
By connecting these points in pairs, we can draw 3 line segments:
1. Segment AB
2. Segment BC
3. Segment CA
So, we can make exactly three line segments. Together, these segments form a triangle.
In simple words: When three points are not in a straight line, we can join them to make 3 segments. These form a triangle.

Exam Tip: Remind yourself that "non-collinear" means the points are not in a line. Joining three such points will always give you a triangle with 3 sides.

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Question 5. Construct two line segments AB and CD of lengths 2.5 cm and 3.2 cm. Construct another segment EF whose length is the sum of these two segments. Measure the new length.
Answer: Let's write down the given lengths:
\( \text{AB} = 2.5\text{ cm} \)
\( \text{CD} = 3.2\text{ cm} \)
To find the length of the new segment EF:
\( \text{Length of EF} = \text{AB} + \text{CD} = 2.5\text{ cm} + 3.2\text{ cm} = 5.7\text{ cm} \)
Steps to draw it:
1. Draw a long ray with a starting point E.
2. Measure 2.5 cm with a compass using a ruler. Put the compass tip on E and mark a point P.
3. Now open the compass to 3.2 cm. Place the compass tip on P and mark another point F on the same line.
4. This gives us the final segment EF.
5. When we measure EF with a ruler, we find that its length is 5.7 cm.
In simple words: The new line EF is made by joining the 2.5 cm line and the 3.2 cm line. Its total length is 5.7 cm.

Exam Tip: When adding segments using a compass, always place the compass needle on the intermediate point (here, P) to copy the second length accurately.

Question 6. If AB = 5.2 cm and CD = 3.6 cm Construct a segment whose length is equal to
(a) AB + 2 CD
(b) AB - CD
(c) 2 CD - AB
Answer: We have the following given lengths:
\( \text{AB} = 5.2\text{ cm} \)
\( \text{CD} = 3.6\text{ cm} \)

(a) For \( \text{AB} + 2 \text{CD} \):
Length = \( 5.2\text{ cm} + 2 \times 3.6\text{ cm} = 5.2\text{ cm} + 7.2\text{ cm} = 12.4\text{ cm} \)
Draw a segment of length 12.4 cm.

(b) For \( \text{AB} - \text{CD} \):
Length = \( 5.2\text{ cm} - 3.6\text{ cm} = 1.6\text{ cm} \)
Draw a segment of length 1.6 cm.

(c) For \( 2 \text{CD} - \text{AB} \):
Length = \( 2 \times 3.6\text{ cm} - 5.2\text{ cm} = 7.2\text{ cm} - 5.2\text{ cm} = 2.0\text{ cm} \)
Draw a segment of length 2 cm.
In simple words: We calculate each length by adding or subtracting. Then we draw lines that match these calculated sizes.

Exam Tip: Write down your arithmetic steps clearly so the examiner can see how you calculated the required lengths before drawing them.

Question 7. Measure the length and width or height of
(a) notebook
(b) pencil
(c) duster.
Answer: We can find these sizes by measuring normal school items with a ruler. Here are typical measurements:
(a) Notebook: Length = 25 cm, Width = 18 cm
(b) Pencil: Length = 15 cm, Width = 0.7 cm
(c) Duster: Length = 15 cm, Width = 5 cm, Height = 4 cm
In simple words: Use your scale to measure these items in real life. The exact numbers may be slightly different for your own things.

Exam Tip: Remember that thick three-dimensional items like a duster have three measurements: length, width, and height.

Question 8. How many line segments are there in the following figure
Answer: To find all the line segments on a line with five points, we pair them up in every possible way:
1. Segments starting with A: AB, AC, AD, and AE (4 segments)
2. Segments starting with B: BC, BD, and BE (3 segments)
3. Segments starting with C: CD and CE (2 segments)
4. Segment starting with D: DE (1 segment)
Now we add these segments together:
Total = 4 + 3 + 2 + 1 = 10 segments
So, there are exactly 10 line segments in the given figure.
In simple words: We list every line that joins any two points. Adding them all up gives us 10 segments in total.

Exam Tip: A systematic way to count is to start from the leftmost point and move right. This avoids counting any segment twice or missing any.

Question 9. Construct a line segment AB of length 7.2 cm. From this cut a segment of 3.2 cm. Measure the remaining length
Answer: Let's write down the given measurements:
Total length of segment AB = 7.2 cm
Length of the cut-off part (let's call it AC) = 3.2 cm
To find the length of the remaining part (CB):
\( \text{Remaining length} = \text{AB} - \text{AC} = 7.2\text{ cm} - 3.2\text{ cm} = 4.0\text{ cm} \)
How to construct this:
1. Draw a line segment AB of length 7.2 cm using a ruler.
2. Use a compass to measure 3.2 cm on your ruler.
3. Put the compass tip on A and make an arc on the segment AB. Let's call this point C.
4. The remaining segment CB is the portion left over.
5. Measuring CB with a ruler gives a length of exactly 4.0 cm.
In simple words: When we take away 3.2 cm from a 7.2 cm line, we are left with a 4.0 cm line.

Exam Tip: Remember to always check your final drawing with a ruler to ensure your calculations match your visual measurement.

Question 10. Verify by measurement that PR + QS = PS + QR
Answer: Let's choose four points P, Q, R, and S in a straight line. If we measure the distance between them, we might get these values:
\( \text{PQ} = 2\text{ cm} \)
\( \text{QR} = 3\text{ cm} \)
\( \text{RS} = 4\text{ cm} \)
Using these values, we can calculate the other segment lengths:
\( \text{PR} = \text{PQ} + \text{QR} = 2\text{ cm} + 3\text{ cm} = 5\text{ cm} \)
\( \text{QS} = \text{QR} + \text{RS} = 3\text{ cm} + 4\text{ cm} = 7\text{ cm} \)
\( \text{PS} = \text{PQ} + \text{QR} + \text{RS} = 2\text{ cm} + 3\text{ cm} + 4\text{ cm} = 9\text{ cm} \)

Now let's check both sides of our equation:
Left-hand side (L.H.S.) = \( \text{PR} + \text{QS} = 5\text{ cm} + 7\text{ cm} = 12\text{ cm} \)
Right-hand side (R.H.S.) = \( \text{PS} + \text{QR} = 9\text{ cm} + 3\text{ cm} = 12\text{ cm} \)

Since L.H.S. = R.H.S. (12 cm = 12 cm), the relation is verified.
In simple words: When we add the lengths PR and QS together, we get the exact same total as adding PS and QR. This means the rule is correct.

Exam Tip: For any verification question, write down L.H.S. and R.H.S. calculations separately before showing they are equal.