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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 geometrical instruments.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 9
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Practical Geometry involves constructing geometrical figures accurately from given measurements. For constructing a quadrilateral, students need to understand which measurements are sufficient and how those measurements can be used in a logical sequence.
The construction may involve sides, angles, diagonals, arcs, and appropriate geometrical instruments. Careful measurement and verification are essential for obtaining the required figure.
This Practice Set 9 contains 5 fresh and challenging MCQs based on NCERT concepts related to quadrilateral construction and geometrical reasoning.
What You Will Learn
✔ Understanding construction conditions
✔ Using diagonals in quadrilateral construction
✔ Applying given angles and side lengths
✔ Understanding the role of compass and protractor
✔ Identifying valid construction methods
✔ Checking geometrical constructions
Why This Topic Is Important
Practical Geometry helps students convert mathematical information into accurate geometrical figures. It develops precision, logical thinking, and spatial understanding.
Understanding the construction process also makes it easier to solve examination questions involving quadrilaterals and related figures.
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 quadrilateral $$ABCD$$ is to be constructed when the lengths of all four sides and one diagonal $$AC$$ are known. What is the most useful first step?
A) Construct diagonal $$AC$$
B) Draw a random angle
C) Draw a circle without a specified radius
D) Construct the perimeter first
Answer:
A) Construct diagonal $$AC$$
Useful Concept
When a diagonal and all four sides of a quadrilateral are known, the diagonal can be used as the initial line segment.
Solution
Suppose the given measurements are:
$$AB=a$$
$$BC=b$$
$$CD=c$$
$$DA=d$$
and:
$$AC=e$$
Since the length of diagonal $$AC$$ is known, it can be drawn first.
After constructing $$AC$$, the remaining vertices can be located using the given side lengths and appropriate arcs.
The diagonal divides the quadrilateral into two triangles:
$$\triangle ABC$$
and:
$$\triangle ADC$$
Therefore, constructing the known diagonal first is a suitable starting step.
Hence, the correct answer is:
A) Construct diagonal $$AC$$
Q2. A student has constructed $$AB=6\text{ cm}$$. The required angle at $$B$$ is $$70^\circ$$. Which point should be the vertex of the angle?
A) $$A$$
B) $$B$$
C) $$C$$
D) Any point
Answer:
**B) $$B$$
Useful Concept
An angle is constructed at the vertex specified in the question.
Solution
The given side is:
$$AB=6\text{ cm}$$
The question specifies that the required angle is at:
$$B$$
Therefore, the vertex of the angle must be point $$B$$.
The angle:
$$70^\circ$$
should be constructed with one arm along the appropriate direction from $$B$$.
Hence, the correct answer is:
B) $$B$$
Q3. Suppose an arc is drawn with centre $$A$$ and radius $$7\text{ cm}$$. Which statement is correct about every point on this arc?
A) Every point is $$7\text{ cm}$$ from $$A$$
B) Every point is $$14\text{ cm}$$ from $$A$$
C) Every point is $$7^\circ$$ from $$A$$
D) Every point is at a different distance from $$A$$
Answer:
A) Every point is $$7\text{ cm}$$ from $$A$$
Useful Concept
All points on a circle or arc are at the same distance from its centre.
Solution
The centre of the arc is:
$$A$$
and its radius is:
$$7\text{ cm}$$
Therefore, for every point $$P$$ on the arc:
$$AP=7\text{ cm}$$
The distance remains constant because the radius of a circle is constant.
Hence, the correct answer is:
A) Every point is $$7\text{ cm}$$ from $$A$$
Q4. A quadrilateral has a diagonal of length $$10\text{ cm}$$. If the diagonal is used as the common side of two triangles, which vertices does it connect?
A) Two adjacent vertices
B) Two opposite vertices
C) Three vertices
D) No vertices
Answer:
B) Two opposite vertices
Useful Concept
A diagonal of a quadrilateral connects two non-adjacent or opposite vertices.
Solution
Consider quadrilateral:
$$ABCD$$
Its diagonals are:
$$AC$$
and:
$$BD$$
The vertices $$A$$ and $$C$$ are opposite vertices, and the segment:
$$AC$$
is a diagonal.
Similarly, $$BD$$ connects the other pair of opposite vertices.
Thus, a diagonal connects two opposite vertices and can divide the quadrilateral into two triangles.
Hence, the correct answer is:
B) Two opposite vertices
Q5. Which sequence is most appropriate when constructing a figure using a given side, an angle, and another side length?
A) Draw the given side → construct the angle → mark the second side
B) Mark the second side → erase the first side → construct the angle
C) Draw the angle anywhere → choose the side length later
D) Draw all lines randomly and measure afterward
Answer:
A) Draw the given side → construct the angle → mark the second side
Useful Concept
Construction should follow the given information in a logical sequence.
Solution
Suppose:
$$AB=7\text{ cm}$$
is given, followed by:
$$\angle ABC=60^\circ$$
and:
$$BC=5\text{ cm}$$
A suitable sequence is:
Step 1: Draw:
$$AB=7\text{ cm}$$
Step 2: At $$B$$, construct:
$$\angle ABC=60^\circ$$
Step 3: On the constructed ray, mark:
$$BC=5\text{ cm}$$
This sequence uses each given measurement in the appropriate order.
Hence, the correct answer is:
A) Draw the given side → construct the angle → mark the second side
Important Concepts
Diagonal of a Quadrilateral
A diagonal joins two opposite vertices.
For quadrilateral:
$$ABCD$$
the diagonals are:
$$AC$$
and:
$$BD$$
Radius of an Arc
If an arc has centre $$A$$ and radius:
$$7\text{ cm}$$
then every point on that arc is:
$$7\text{ cm}$$
from $$A$$.
Angle at a Vertex
If the question specifies:
$$\angle ABC=70^\circ$$
then the angle must be constructed at vertex:
$$B$$
Construction Sequence
A logical construction sequence may involve:
- Drawing a known side.
- Constructing the required angle.
- Marking the next known length.
- Using arcs to locate remaining points.
- Joining the required vertices.
- Verifying the construction.
Diagonal as Common Side
A diagonal can divide a quadrilateral into two triangles.
For example:
$$AC$$
divides quadrilateral $$ABCD$$ into:
$$\triangle ABC$$
and:
$$\triangle ADC$$
Related Practice Questions
Q1. Name the diagonals of quadrilateral:
$$PQRS$$
Q2. If an arc has radius:
$$8\text{ cm}$$
what is the distance of every point on the arc from its centre?
Q3. At which point is:
$$\angle PQR$$
constructed?
Q4. Why can a diagonal help in constructing a quadrilateral?
Q5. What should be done after completing all construction steps?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which segment is a diagonal of quadrilateral $$ABCD$$?
A) $$AB$$
B) $$BC$$
C) $$AC$$
D) $$AD$$
Q2. An arc has centre $$O$$ and radius:
$$6\text{ cm}$$
Every point on the arc is:
A) $$3\text{ cm}$$ from $$O$$
B) $$6\text{ cm}$$ from $$O$$
C) $$12\text{ cm}$$ from $$O$$
D) At any distance from $$O$$
Q3. In:
$$\angle XYZ=80^\circ$$
the vertex is:
A) $$X$$
B) $$Y$$
C) $$Z$$
D) None
Q4. A diagonal of a quadrilateral can divide it into:
A) Two triangles
B) Three circles
C) Four squares
D) Two lines only
Q5. Which should generally come first in a construction when its length is directly given?
A) Constructing the given line segment
B) Colouring the figure
C) Erasing the paper
D) Drawing random arcs
Exam Tips
✔ Read all given measurements before beginning.
✔ Start with a directly given side or diagonal whenever appropriate.
✔ Construct angles at the correct vertex.
✔ Use the compass to transfer exact lengths.
✔ Remember that a diagonal joins opposite vertices.
✔ Follow the construction sequence carefully.
✔ Verify the final figure against the original conditions.
Quick Revision Notes
✔ A diagonal connects opposite vertices.
✔ A quadrilateral has two diagonals.
✔ A diagonal can divide a quadrilateral into two triangles.
✔ Every point on an arc is at a fixed distance from its centre.
✔ An angle must be constructed at its specified vertex.
✔ Construction should follow a logical sequence.
✔ All given measurements should be verified after construction.
Common Mistakes Students Make
❌ Constructing an angle at the wrong vertex.
❌ Confusing a diagonal with a side.
❌ Using an incorrect compass radius.
❌ Starting construction without identifying the given measurements.
❌ Joining the wrong vertices.
❌ Not checking the final figure against the conditions.
Key Takeaways
✔ Diagonals are important in quadrilateral construction.
✔ A diagonal joins opposite vertices.
✔ A diagonal can divide a quadrilateral into two triangles.
✔ The radius of an arc determines the distance from its centre.
✔ Angles must be constructed at the correct vertices.
✔ A systematic construction sequence improves accuracy.
FAQs
Q. What is a diagonal of a quadrilateral?
Answer:
A diagonal is a line segment joining two opposite vertices of a quadrilateral.
Q. How many diagonals does a quadrilateral have?
Answer:
A quadrilateral has two diagonals.
Q. Why can a diagonal be used during construction?
Answer:
A diagonal can divide a quadrilateral into two triangles, making it easier to construct the figure using known measurements.
Q. What does the radius of an arc represent?
Answer:
It represents the fixed distance between the centre and every point on the arc.
Q. Why is construction order important?
Answer:
Following a logical order ensures that each given measurement is used correctly and helps produce an accurate figure.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on diagonals, arcs, angles, side lengths, and systematic construction methods.
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