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Practice Class 8 Maths Chapter 4 Practical Geometry MCQ Questions with Answers and Solutions based on NCERT concepts. Solve fresh questions on quadrilateral construction, sides, angles, diagonals, and construction methods.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 6
Difficulty Level: Moderate to Difficult
Based On: NCERT Mathematics
Introduction
A geometrical construction is successful only when the given conditions are carefully followed. In the construction of quadrilaterals, students need to understand how different measurements are related and how they can be used to locate the required vertices.
Depending on the information given, a construction may involve drawing a side first, constructing an angle, transferring a length with a compass, or using a diagonal to divide the figure into triangles.
This Practice Set 6 contains 5 fresh MCQs based on these important construction ideas.
What You Will Learn
✔ Understanding construction sequences
✔ Using a compass to transfer measurements
✔ Locating vertices using given information
✔ Understanding the relationship between sides and angles
✔ Identifying correct construction steps
✔ Applying geometrical reasoning
Why This Topic Is Important
Practical Geometry is not only about knowing the properties of figures; it also requires students to understand how a figure can be constructed.
Learning the correct sequence of construction steps improves accuracy and helps students solve construction questions confidently.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ NCERT-Based Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Mathematics Revision
✔ Geometry Practice
Q1. A student has to construct a line segment of length $$6\text{ cm}$$ and then transfer this same length to another location. Which instrument is most useful for transferring the length?
A) Protractor
B) Compass
C) Ruler only
D) Set square
Answer:
B) Compass
Useful Concept
A compass can be used to transfer a known length from one location to another without changing its measure.
Solution
Suppose a line segment:
$$AB=6\text{ cm}$$
has already been drawn.
To transfer the same length to another location, the compass can be opened to the length:
$$AB$$
and then used to mark the same distance elsewhere.
This avoids repeatedly measuring the length with a ruler.
Therefore, the correct answer is:
B) Compass
Q2. While constructing a quadrilateral, a student has correctly drawn one side and then constructs the required angle at one endpoint. What should generally be done next if the length of the next side is known?
A) Draw the next side along the constructed ray
B) Erase the first side
C) Draw a circle around the figure
D) Change the given angle
Answer:
A) Draw the next side along the constructed ray
Useful Concept
After constructing an angle, the required side can be marked along the appropriate ray using its given length.
Solution
Suppose the first side is:
$$AB$$
and an angle is constructed at:
$$B$$
The next side must start from:
$$B$$
and follow the ray representing the required angle.
If its length is given as:
$$BC=5\text{ cm}$$
then the point $$C$$ is marked on that ray at a distance of:
$$5\text{ cm}$$
from $$B$$.
Thus, the next step is to draw or mark the next side along the constructed ray.
Hence, the correct answer is:
A) Draw the next side along the constructed ray
Q3. A compass is set to the distance between two points $$P$$ and $$Q$$. If the compass opening is kept unchanged, what does it represent?
A) The angle between $$P$$ and $$Q$$
B) The length $$PQ$$
C) The area of the figure
D) The perimeter of the figure
Answer:
B) The length $$PQ$$
Useful Concept
The opening of a compass represents the distance between its two tips.
Solution
Suppose the distance between two points is:
$$PQ=4\text{ cm}$$
When the compass is adjusted so that its tips coincide with $$P$$ and $$Q$$, its opening represents the length:
$$PQ$$
If the opening is kept unchanged, the same length can be transferred to another position.
Therefore, the correct answer is:
B) The length $$PQ$$
Q4. Which of the following is the most appropriate reason for keeping construction arcs visible until the construction is complete?
A) They make the diagram colourful
B) They help identify points obtained from intersections
C) They increase the size of the figure
D) They replace the need for measurements
Answer:
B) They help identify points obtained from intersections
Useful Concept
Construction arcs and lines provide important guides for locating points accurately.
Solution
During construction, arcs are often drawn to locate points at a specified distance.
For example, an intersection of two arcs may determine the position of a required vertex.
If these construction marks are erased too early, it becomes more difficult to verify how the point was obtained.
Therefore, construction arcs should generally remain visible until the construction has been checked.
Hence, the correct answer is:
B) They help identify points obtained from intersections
Q5. Two arcs intersect at a point $$R$$ during a construction. What does this intersection usually indicate?
A) A point satisfying the distance conditions represented by the arcs
B) The centre of every circle
C) The midpoint of every side
D) The perimeter of the figure
Answer:
A) A point satisfying the distance conditions represented by the arcs
Useful Concept
The intersection of arcs can locate a point that is at specified distances from the centres of those arcs.
Solution
Suppose one arc is drawn with centre:
$$P$$
and another with centre:
$$Q$$
If they intersect at:
$$R$$
then the point $$R$$ satisfies the distances represented by the two arcs.
For example:
$$PR=5\text{ cm}$$
and:
$$QR=4\text{ cm}$$
if the corresponding radii were used.
Thus, the intersection helps locate the required point.
Hence, the correct answer is:
A) A point satisfying the distance conditions represented by the arcs
Important Concepts
Compass as a Length Transfer Tool
A compass can transfer a given length from one position to another.
For example, if:
$$AB=5\text{ cm}$$
the same length can be transferred without measuring it again.
Construction Ray
After constructing an angle, a ray provides the direction along which the next side can be drawn.
Construction Arcs
Arcs are used to locate points at specified distances from given points.
Intersection of Arcs
The intersection of two arcs can determine the position of a required point.
Construction Accuracy
Construction lines and arcs should be drawn carefully so that the required points can be located accurately.
Related Practice Questions
Q1. If:
$$AB=7\text{ cm}$$
how can this length be transferred to another location?
Q2. What does the opening of a compass represent?
Q3. Why are construction arcs useful?
Q4. What can the intersection of two arcs determine?
Q5. Why should construction marks be checked before erasing them?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which instrument is most useful for transferring a given length?
A) Protractor
B) Compass
C) Ruler only
D) Pencil
Q2. If a compass is set to:
$$AB=5\text{ cm}$$
its opening represents:
A) $$5^\circ$$
B) $$5\text{ cm}$$
C) $$10\text{ cm}$$
D) $$50\text{ cm}$$
Q3. Why are arcs used in construction?
A) To locate points
B) To decorate the figure
C) To colour the figure
D) To calculate area only
Q4. Two arcs intersect at point $$X$$. What can this point represent?
A) A point satisfying given distance conditions
B) Always the midpoint
C) Always the centre
D) Always a vertex of a square
Q5. After constructing an angle and knowing the next side length, the side should be:
A) Drawn along the appropriate ray
B) Drawn randomly
C) Erased
D) Replaced by an arc
Exam Tips
✔ Use the compass carefully when transferring lengths.
✔ Keep the compass opening unchanged while transferring a particular length.
✔ Use construction arcs to locate points accurately.
✔ Do not erase important construction marks before checking your work.
✔ Follow the construction sequence systematically.
✔ Always verify the final figure against the measurements given in the question.
Quick Revision Notes
✔ Compass can transfer lengths.
✔ Ruler is used to draw and measure line segments.
✔ Protractor is used to measure and construct angles.
✔ Construction arcs help locate points.
✔ Intersection of arcs can determine a required point.
✔ After constructing an angle, the next side can be marked along the corresponding ray.
✔ Accurate construction requires careful use of instruments.
Common Mistakes Students Make
❌ Changing the compass opening while transferring the same length.
❌ Drawing the next side in the wrong direction.
❌ Ignoring the intersection of construction arcs.
❌ Erasing construction marks before checking the figure.
❌ Using a protractor when a compass is required to transfer a length.
❌ Drawing arcs too small to identify their intersection clearly.
Key Takeaways
✔ A compass is useful for transferring lengths.
✔ The opening of a compass represents a distance.
✔ Construction arcs help locate points.
✔ Intersections of arcs can determine required vertices.
✔ Construction rays provide the direction for drawing sides.
✔ Keeping construction marks visible helps verify the construction.
FAQs
Q. What is the purpose of a compass in geometrical construction?
Answer:
A compass is used to draw arcs and circles and to transfer given lengths accurately from one location to another.
Q. What does the opening of a compass represent?
Answer:
The opening represents the distance between the two tips of the compass.
Q. Why are arcs used during construction?
Answer:
Arcs can help locate points that are at specified distances from given points.
Q. What does the intersection of two arcs indicate?
Answer:
It can indicate a point that satisfies the distance conditions represented by the two arcs.
Q. Why should construction marks not be erased immediately?
Answer:
They help verify the steps and identify points obtained during the construction.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on compass usage, transferring lengths, construction arcs, rays, and locating points through intersections.
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