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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, diagonals, angles, sides, and construction techniques.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 7
Difficulty Level: Moderate to Difficult
Based On: NCERT Mathematics
Introduction
In practical geometry, the information provided in a question determines the method used for constructing a geometrical figure. Students need to understand how given sides, angles, and diagonals can be combined to locate the required vertices.
A successful construction involves following the measurements in the correct order and using the appropriate instrument for each step.
This Practice Set 7 focuses on construction sequences, intersections, angle construction, and checking whether a completed quadrilateral satisfies the given conditions.
What You Will Learn
✔ Understanding construction sequences
✔ Locating vertices using arcs
✔ Applying angle construction
✔ Using given side lengths correctly
✔ Verifying a completed construction
✔ Identifying errors in construction
Why This Topic Is Important
Practical Geometry develops accuracy as well as logical thinking. Students must not only know the properties of a quadrilateral but also understand how each measurement helps in constructing the figure.
These skills are useful for both theoretical MCQs and practical construction questions.
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 constructs a line segment $$AB=8\text{ cm}$$. At point $$A$$, an angle of $$60^\circ$$ is constructed. If the next side has length $$5\text{ cm}$$, where should the endpoint of this side be marked?
A) At any point on the page
B) On the constructed ray at a distance of $$5\text{ cm}$$ from $$A$$
C) On $$AB$$ itself
D) At the midpoint of $$AB$$
Answer:
B) On the constructed ray at a distance of $$5\text{ cm}$$ from $$A$$
Useful Concept
When a side length and an angle are given, the endpoint of the side is located along the ray forming the required angle.
Solution
The first side is:
$$AB=8\text{ cm}$$
At point $$A$$, an angle of:
$$60^\circ$$
is constructed.
The next side has length:
$$5\text{ cm}$$
Therefore, the endpoint must be marked on the constructed ray at a distance of:
$$5\text{ cm}$$
from point $$A$$.
Hence, the correct answer is:
B) On the constructed ray at a distance of $$5\text{ cm}$$ from $$A$$
Q2. During a construction, two arcs are drawn from points $$A$$ and $$B$$ with appropriate radii. Their intersection gives point $$C$$. What does this construction ensure?
A) $$C$$ is at the required distances from $$A$$ and $$B$$
B) $$C$$ is always the midpoint of $$AB$$
C) $$C$$ must lie on $$AB$$
D) $$C$$ is always the centre of a circle
Answer:
A) $$C$$ is at the required distances from $$A$$ and $$B$$
Useful Concept
An arc represents all points at a fixed distance from its centre.
Solution
Suppose an arc is drawn with centre $$A$$ and radius:
$$r_1$$
Then every point on that arc is at distance:
$$r_1$$
from $$A$$.
Similarly, an arc with centre $$B$$ and radius:
$$r_2$$
contains points at distance:
$$r_2$$
from $$B$$.
If the two arcs intersect at $$C$$, then:
$$AC=r_1$$
and:
$$BC=r_2$$
Therefore, point $$C$$ satisfies both required distance conditions.
Hence, the correct answer is:
A) $$C$$ is at the required distances from $$A$$ and $$B$$
Q3. A student completes a quadrilateral construction. Which is the best way to check whether the construction is correct?
A) Check whether the figure looks attractive
B) Verify the given lengths and angles
C) Check the colour of the diagram
D) Count the number of pencils used
Answer:
B) Verify the given lengths and angles
Useful Concept
A construction is correct when it satisfies the measurements and conditions given in the question.
Solution
Suppose a question gives:
$$AB=6\text{ cm}$$
and:
$$\angle A=75^\circ$$
After completing the construction, the student should verify whether the constructed figure satisfies the given conditions.
The appearance of the figure alone is not sufficient.
Therefore, the correct way to check the construction is to verify the required lengths, angles, and other given measurements.
Hence, the correct answer is:
B) Verify the given lengths and angles
Q4. If a construction requires a point to be at a distance of $$4\text{ cm}$$ from point $$P$$, which construction can represent all possible positions of such a point?
A) A circle with centre $$P$$ and radius $$4\text{ cm}$$
B) A line of length $$4\text{ cm}$$ only
C) A point at $$P$$
D) An angle of $$4^\circ$$
Answer:
A) A circle with centre $$P$$ and radius $$4\text{ cm}$$
Useful Concept
Every point on a circle is at the same distance from its centre.
Solution
The required distance is:
$$4\text{ cm}$$
from point $$P$$.
If a circle is drawn with:
Centre: $$P$$
Radius: $$4\text{ cm}$$
then every point on that circle is exactly:
$$4\text{ cm}$$
from $$P$$.
Therefore, this circle represents all possible positions satisfying the distance condition.
Hence, the correct answer is:
A) A circle with centre $$P$$ and radius $$4\text{ cm}$$
Q5. A student is constructing a quadrilateral and accidentally uses a compass opening of $$5\text{ cm}$$ instead of the required $$6\text{ cm}$$. What is the likely result?
A) The construction may not satisfy the required condition
B) The construction will always remain correct
C) The number of vertices will increase
D) The quadrilateral will automatically become a square
Answer:
A) The construction may not satisfy the required condition
Useful Concept
The compass opening represents the length being transferred. Therefore, an incorrect opening can produce an incorrect distance.
Solution
The required length is:
$$6\text{ cm}$$
but the compass has been set to:
$$5\text{ cm}$$
Therefore, the transferred length will be:
$$5\text{ cm}$$
instead of:
$$6\text{ cm}$$
This means the required construction condition is not satisfied.
Hence, the correct answer is:
A) The construction may not satisfy the required condition
Important Concepts
Circle as a Locus of Equal Distance
A circle with centre $$P$$ and radius $$r$$ contains all points that are at distance:
$$r$$
from $$P$$.
Arc Intersection
Two arcs with appropriate centres and radii can intersect at a point satisfying two distance conditions.
Construction Verification
After completing a construction, check:
✔ Given side lengths
✔ Given angles
✔ Given diagonal lengths
✔ Required relationships
Compass Accuracy
If a length is to be transferred, the compass opening must match the required distance.
For example, if:
$$AB=6\text{ cm}$$
the compass should be set to the distance:
$$6\text{ cm}$$
Construction Sequence
A construction should be completed in a logical order, starting from the measurements that are directly given.
Related Practice Questions
Q1. If a point is required to be $$5\text{ cm}$$ from point $$A$$, what circle can be drawn?
Q2. What does the intersection of two appropriate arcs help determine?
Q3. Why should the compass opening be checked before transferring a length?
Q4. What should be checked after completing a quadrilateral construction?
Q5. If:
$$AB=7\text{ cm}$$
what should be the compass opening when transferring $$AB$$?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. A circle with centre $$O$$ and radius $$5\text{ cm}$$ contains points that are:
A) Always $$5\text{ cm}$$ from $$O$$
B) Always $$10\text{ cm}$$ from $$O$$
C) Always at $$5^\circ$$ from $$O$$
D) At any distance from $$O$$
Q2. If two construction arcs intersect at point $$X$$, point $$X$$ can satisfy:
A) Two distance conditions
B) No distance condition
C) Only an angle condition
D) Only a perimeter condition
Q3. If the required compass opening is:
$$7\text{ cm}$$
but it is set to:
$$6\text{ cm}$$
what should be done?
A) Correct the compass opening
B) Continue without correction
C) Change the ruler
D) Change the angle
Q4. A completed construction should be checked against:
A) Given measurements
B) Colour
C) Size of paper
D) Pencil type
Q5. Which instrument helps transfer a specified distance?
A) Compass
B) Protractor
C) Eraser
D) Set square only
Exam Tips
✔ Start construction from the information that is directly given.
✔ Use arcs to locate points at specified distances.
✔ Check the compass opening before transferring a length.
✔ Remember that every point on a circle is at the same distance from its centre.
✔ Verify the final figure against all given conditions.
✔ Keep construction arcs visible until the figure has been checked.
Quick Revision Notes
✔ A circle represents points at a fixed distance from its centre.
✔ Compass opening represents a length.
✔ Two arcs can intersect to locate a required point.
✔ Construction must satisfy the given measurements.
✔ Incorrect compass settings can lead to incorrect constructions.
✔ Completed figures should be verified carefully.
Common Mistakes Students Make
❌ Using the wrong compass opening.
❌ Assuming an arc intersection is always a midpoint.
❌ Forgetting to verify the final construction.
❌ Drawing a circle with the wrong radius.
❌ Ignoring given side lengths or angles.
❌ Erasing construction marks before checking the figure.
Key Takeaways
✔ A circle with centre $$P$$ and radius $$r$$ represents points at distance $$r$$ from $$P$$.
✔ Arcs can be used to locate points.
✔ The intersection of arcs can satisfy multiple distance conditions.
✔ Compass settings must be accurate.
✔ A completed construction should always be verified.
✔ Practical Geometry requires both mathematical understanding and measurement accuracy.
FAQs
Q. What does a circle with centre $$P$$ and radius $$4\text{ cm}$$ represent?
Answer:
It represents all points that are exactly:
$$4\text{ cm}$$
from point $$P$$.
Q. Why are two arcs sometimes used in construction?
Answer:
Two arcs can intersect at a point that satisfies the distance requirements from two different points.
Q. What happens if the compass opening is incorrect?
Answer:
The transferred length will be incorrect, and the final construction may not satisfy the given conditions.
Q. How can a completed construction be checked?
Answer:
The constructed lengths, angles, diagonals, and other required conditions should be verified against the measurements given in the question.
Q. Why should construction arcs be kept visible?
Answer:
They help identify how points were located and make it easier to verify the construction.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on circles, arcs, compass settings, construction sequences, and verification of geometrical figures.
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