Welcome To My School Study
Practice Class 8 Maths Chapter 4 Practical Geometry MCQ Questions with Answers and Solutions based on NCERT concepts. Solve fresh and challenging MCQs on quadrilateral construction, diagonals, angles, sides, and geometrical instruments.
Do You Know
Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 13
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Practical Geometry focuses on constructing geometrical figures accurately from given measurements. In quadrilateral construction, students need to recognise the available information and select a suitable sequence of steps.
A construction may involve known sides, angles, diagonals, and distances. Correct use of a ruler, compass, and protractor helps ensure that every condition is satisfied.
This Practice Set 13 contains 5 fresh and challenging MCQs based on NCERT concepts of quadrilateral construction and geometrical reasoning.
What You Will Learn
✔ Identifying construction conditions
✔ Using diagonals to construct quadrilaterals
✔ Understanding the role of arcs
✔ Constructing and interpreting angles
✔ Checking construction accuracy
✔ Applying practical geometry concepts
Why This Topic Is Important
Practical Geometry develops precision, spatial reasoning, and mathematical thinking. Students learn how a geometrical figure can be determined from suitable combinations of measurements.
These skills are useful for construction-based questions in school examinations.
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 $$PQRS$$ is given with:
$$PQ=6\text{ cm}$$
$$QR=5\text{ cm}$$
$$RS=7\text{ cm}$$
$$SP=4\text{ cm}$$
and:
$$PR=8\text{ cm}$$
Which measurement acts as the diagonal in this construction?
A) $$PQ$$
B) $$QR$$
C) $$PR$$
D) $$RS$$
Answer:
C) $$PR$$
Useful Concept
A diagonal joins two opposite vertices of a quadrilateral.
Solution
The quadrilateral is:
$$PQRS$$
Its opposite vertex pairs are:
$$P,R$$
and:
$$Q,S$$
Therefore:
$$PR$$
is a diagonal.
The given measurement:
$$PR=8\text{ cm}$$
is therefore the diagonal used in the construction.
Hence, the correct answer is:
C) $$PR$$
Q2. An arc with centre $$A$$ and radius $$9\text{ cm}$$ is drawn. Point $$B$$ lies on the arc. Which equation represents the distance between $$A$$ and $$B$$?
A) $$AB=3\text{ cm}$$
B) $$AB=9\text{ cm}$$
C) $$AB=18\text{ cm}$$
D) $$AB=0\text{ cm}$$
Answer:
B) $$AB=9\text{ cm}$$
Useful Concept
Every point on an arc is at a distance equal to the radius from its centre.
Solution
The centre of the arc is:
$$A$$
The radius is:
$$9\text{ cm}$$
Since $$B$$ lies on the arc:
$$AB=9\text{ cm}$$
Therefore, the correct relation is:
$$AB=9\text{ cm}$$
Hence, the correct answer is:
B) $$AB=9\text{ cm}$$
Q3. In constructing a quadrilateral, a student first draws a known diagonal $$AC$$. The next step is to locate point $$B$$ using the known lengths $$AB$$ and $$BC$$. Which construction method is most appropriate?
A) Draw two arcs with centres $$A$$ and $$C$$
B) Draw an arc with centre $$B$$
C) Construct an angle at an arbitrary point
D) Draw a circle without using a radius
Answer:
A) Draw two arcs with centres $$A$$ and $$C$$
Useful Concept
A point at known distances from two fixed points can be located using intersecting arcs.
Solution
The diagonal:
$$AC$$
has already been constructed.
The required point $$B$$ must satisfy:
$$AB=\text{given length}$$
and:
$$BC=\text{given length}$$
Therefore:
- Draw an arc with centre $$A$$ and radius equal to the given $$AB$$.
- Draw another arc with centre $$C$$ and radius equal to the given $$BC$$.
- Their intersection gives the possible position of $$B$$.
Hence, the correct answer is:
A) Draw two arcs with centres $$A$$ and $$C$$
Q4. A student is constructing a quadrilateral and needs to draw:
$$\angle ABC=80^\circ$$
Which statement is correct?
A) The angle must be constructed at $$A$$
B) The angle must be constructed at $$B$$
C) The angle must be constructed at $$C$$
D) The angle can be constructed anywhere
Answer:
B) The angle must be constructed at $$B$$
Useful Concept
The middle letter in the name of an angle represents its vertex.
Solution
The given angle is:
$$\angle ABC$$
The middle letter is:
$$B$$
Therefore, $$B$$ is the vertex.
The angle:
$$80^\circ$$
must be constructed at point $$B$$.
Hence, the correct answer is:
B) The angle must be constructed at $$B$$
Q5. A student constructs a quadrilateral using four given sides and one diagonal. After completing it, all four sides are correct but the diagonal is incorrect. What does this indicate?
A) The construction needs to be checked and corrected
B) The diagonal can always be ignored
C) Only the angles matter
D) The four sides automatically make every construction correct
Answer:
A) The construction needs to be checked and corrected
Useful Concept
All given conditions must be satisfied in a geometrical construction.
Solution
The construction is based on:
Four sides + one diagonal
Therefore, the diagonal is an essential part of the given information.
If the four sides are correct but the diagonal does not match the specified length, then the constructed figure does not satisfy all the required conditions.
The student should check:
✔ Compass setting
✔ Position of vertices
✔ Measurement of the diagonal
✔ Construction sequence
Therefore, the construction needs to be checked and corrected.
Hence, the correct answer is:
A) The construction needs to be checked and corrected
Important Concepts
Diagonal
A diagonal connects two opposite vertices.
For quadrilateral:
$$PQRS$$
the diagonals are:
$$PR$$
and:
$$QS$$
Locating a Point Using Two Distances
If point $$B$$ must satisfy:
$$AB=a$$
and:
$$CB=b$$
then two arcs can be drawn with centres $$A$$ and $$C$$ and radii $$a$$ and $$b$$ respectively.
Their intersection gives the possible location of $$B$$.
Angle Notation
For:
$$\angle ABC$$
the vertex is:
$$B$$
Verification
Every given condition must be satisfied after completing the construction.
Construction Accuracy
A correct construction requires accurate:
✔ Lengths
✔ Angles
✔ Compass settings
✔ Vertex positions
Related Practice Questions
Q1. Identify the diagonals of quadrilateral $$WXYZ$$.
Q2. If an arc has radius:
$$8\text{ cm}$$
what is the distance from its centre to any point on it?
Q3. In $$\angle PQR$$, which point is the vertex?
Q4. How can a point be located at two specified distances from two fixed points?
Q5. Why must the diagonal be checked after completing a quadrilateral construction?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which is a diagonal of quadrilateral $$ABCD$$?
A) $$AB$$
B) $$BC$$
C) $$AC$$
D) $$CD$$
Q2. An arc has centre $$O$$ and radius:
$$10\text{ cm}$$
A point $$P$$ on the arc satisfies:
A) $$OP=5\text{ cm}$$
B) $$OP=10\text{ cm}$$
C) $$OP=20\text{ cm}$$
D) $$OP=0\text{ cm}$$
Q3. In:
$$\angle RST$$
the vertex is:
A) $$R$$
B) $$S$$
C) $$T$$
D) None
Q4. A point is required to be $$5\text{ cm}$$ from $$A$$ and $$7\text{ cm}$$ from $$C$$. What can locate the point?
A) Two suitable arcs
B) One random line
C) One angle only
D) An eraser
Q5. If a required diagonal does not have the given length after construction, what should be done?
A) Check the construction
B) Ignore the diagonal
C) Change the given length
D) Stop checking
Exam Tips
✔ Identify opposite vertices before identifying diagonals.
✔ Use two arcs when a point must satisfy two distance conditions.
✔ Remember that the middle letter of an angle is its vertex.
✔ Keep the compass opening unchanged when transferring a required length.
✔ Verify the diagonal as well as all four sides.
✔ Correct construction errors before finalising the figure.
Quick Revision Notes
✔ Diagonal joins opposite vertices.
✔ In $$PQRS$$, diagonals are:
$$PR$$
and:
$$QS$$
✔ An arc represents a fixed distance from its centre.
✔ In $$\angle ABC$$, vertex is:
$$B$$
✔ Two arcs can locate a point satisfying two distance conditions.
✔ All given measurements must be verified.
Common Mistakes Students Make
❌ Calling an adjacent side a diagonal.
❌ Using the wrong centre for an arc.
❌ Measuring an arc instead of using the required compass radius.
❌ Constructing an angle at the wrong vertex.
❌ Ignoring an incorrect diagonal after construction.
❌ Failing to verify all conditions.
Key Takeaways
✔ Diagonals connect opposite vertices.
✔ Two arcs can locate a point at specified distances from two known points.
✔ The middle letter of an angle is its vertex.
✔ A construction is correct only when all given conditions are satisfied.
✔ Accuracy of compass and ruler measurements is essential.
FAQs
Q. What are the diagonals of quadrilateral $$PQRS$$?
Answer:
The diagonals are:
$$PR$$
and:
$$QS$$
Q. How can point $$B$$ be located if $$AB$$ and $$CB$$ are known?
Answer:
Draw an arc centred at $$A$$ with radius $$AB$$ and another arc centred at $$C$$ with radius $$CB$$. Their intersection gives the possible location of $$B$$.
Q. What is the vertex of $$\angle ABC$$?
Answer:
The vertex is:
$$B$$
Q. Why is the diagonal important in quadrilateral construction?
Answer:
A diagonal provides additional information and can divide the quadrilateral into two triangles, making construction possible.
Q. What should be checked after completing a construction?
Answer:
All given side lengths, angles, diagonals, and other conditions should be checked for accuracy.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based questions covering diagonals, arcs, angle notation, point location, and construction verification.
Related links
- Class 8 Science Chapter 2 Microorganisms Friend and Foe part-7
- Class 8 Social Science Chapter 2 From Trade to Territory part-4
- Class 8 English Chapter 2 A Concrete Example part-4
- Class 8 Maths Chapter 4 Practical Geometry part-13
- Class 8 Science Chapter 2 Microorganisms Friend and Foe part-6
- Class 8 Social Science Chapter 2 From Trade to Territory part-3
- Class 8 English Chapter 2 A Concrete Example part-3
- Class 8 Maths Chapter 4 Practical Geometry part-12
- Class 8 Science Chapter 2 Microorganisms Friend and Foe part-5
Latest Posts
- Class 10 Science Chapter 2 Acids, Bases and Salts
- Class 9 Science Chapter 2 Is Matter Around Us Pure
- Class 7 Science Chapter 2 Nutrition in Animals
- Class 8 Science Chapter 2 Microorganisms Friend and Foe
- Class 8 History Chapter 2 From Trade to Territory
Join Our Other Communities
Instagram , Youtube , Facebook
