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Practice Class 8 Maths Chapter 4 Practical Geometry MCQ Questions with Answers and Solutions based on NCERT concepts. Solve fresh and challenging questions on quadrilateral construction, diagonals, angles, sides, and geometrical instruments.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 12
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Construction of geometrical figures requires accurate use of the information provided in the question. In the construction of quadrilaterals, students need to identify the known sides, angles, and diagonals and then arrange the construction steps logically.
A diagonal is particularly useful because it divides a quadrilateral into two triangles. Once one triangle is constructed, the remaining information can be used to complete the quadrilateral.
This Practice Set 12 contains 5 fresh NCERT-based MCQs focusing on construction conditions, diagonals, arcs, angles, and verification.
What You Will Learn
✔ Understanding quadrilateral construction
✔ Using a diagonal to divide a quadrilateral
✔ Applying compass measurements
✔ Constructing given angles accurately
✔ Identifying sufficient information
✔ Checking the final construction
Why This Topic Is Important
Practical Geometry develops accuracy, logical thinking, and spatial understanding. Students learn how different measurements determine the position and shape of geometrical figures.
These concepts are important for solving construction questions confidently 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 $$ABCD$$ is to be constructed using four sides and one diagonal. If the diagonal $$AC$$ is known, which two triangles are constructed around it?
A) $$\triangle ABC$$ and $$\triangle ACD$$
B) $$\triangle ABD$$ and $$\triangle BCD$$
C) $$\triangle ABC$$ and $$\triangle BCD$$
D) $$\triangle ABD$$ and $$\triangle ACD$$
Answer:
A) $$\triangle ABC$$ and $$\triangle ACD$$
Useful Concept
A diagonal divides a quadrilateral into two triangles.
Solution
Consider quadrilateral:
$$ABCD$$
The diagonal is:
$$AC$$
This diagonal joins opposite vertices $$A$$ and $$C$$.
Therefore, it divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
The common side of both triangles is:
$$AC$$
Hence, the correct answer is:
A) $$\triangle ABC$$ and $$\triangle ACD$$
Q2. A compass is opened to a length of $$6\text{ cm}$$ and an arc is drawn with centre $$O$$. If point $$P$$ lies on this arc, which relation is correct?
A) $$OP=3\text{ cm}$$
B) $$OP=6\text{ cm}$$
C) $$OP=12\text{ cm}$$
D) $$OP=0\text{ cm}$$
Answer:
B) $$OP=6\text{ cm}$$
Useful Concept
The distance from the centre to any point on a circle or arc equals its radius.
Solution
The compass is opened to:
$$6\text{ cm}$$
Therefore, the radius of the arc is:
$$6\text{ cm}$$
Since $$P$$ lies on the arc:
$$OP=6\text{ cm}$$
Hence, the correct answer is:
B) $$OP=6\text{ cm}$$
Q3. A quadrilateral is to be constructed when three sides and two diagonals are known. Why are the diagonals useful?
A) They help determine the positions of the remaining vertices
B) They determine the colour of the quadrilateral
C) They replace all side measurements
D) They are used only for decoration
Answer:
A) They help determine the positions of the remaining vertices
Useful Concept
Diagonals provide additional distance information needed to locate vertices.
Solution
Suppose three sides and two diagonals of a quadrilateral are given.
The diagonals connect opposite vertices and provide additional measurements.
For example, in:
$$ABCD$$
the diagonals are:
$$AC$$
and:
$$BD$$
Knowing these lengths along with three sides provides enough information to locate the vertices through suitable construction steps.
Therefore, diagonals are useful because they help determine the positions of the remaining vertices.
Hence, the correct answer is:
A) They help determine the positions of the remaining vertices
Q4. A student has drawn $$AB=8\text{ cm}$$ and needs to construct an angle of $$65^\circ$$ at $$B$$. Which ray should contain the next side if the required angle is $$\angle ABC$$?
A) A ray starting from $$A$$
B) A ray starting from $$B$$
C) A ray starting from $$C$$
D) Any ray without a vertex
Answer:
B) A ray starting from $$B$$
Useful Concept
The middle letter in an angle name represents its vertex.
Solution
The given angle is:
$$\angle ABC$$
The middle letter is:
$$B$$
Therefore, the vertex of the angle is $$B$$.
The required angle:
$$65^\circ$$
must be constructed at point $$B$$.
The next side:
$$BC$$
must therefore lie along the ray starting from $$B$$.
Hence, the correct answer is:
B) A ray starting from $$B$$
Q5. A student completes a quadrilateral construction and measures one side as $$7.4\text{ cm}$$, whereas the given measurement was $$7\text{ cm}$$. What should the student conclude?
A) The construction should be checked for accuracy
B) The given measurement must be wrong
C) The difference should always be ignored
D) The side should be renamed
Answer:
A) The construction should be checked for accuracy
Useful Concept
A completed construction should satisfy the given measurements as accurately as possible.
Solution
The required length is:
$$7\text{ cm}$$
but the constructed length is:
$$7.4\text{ cm}$$
The difference is:
$$7.4-7=0.4\text{ cm}$$
This indicates that the construction should be checked.
The student should verify:
✔ Compass opening
✔ Ruler measurement
✔ Position of construction points
✔ Accuracy of arcs and lines
The given measurement should not simply be changed.
Hence, the correct answer is:
A) The construction should be checked for accuracy
Important Concepts
Diagonal
A diagonal joins two opposite vertices of a quadrilateral.
For:
$$ABCD$$
the diagonals are:
$$AC$$
and:
$$BD$$
Diagonal and Triangles
Diagonal:
$$AC$$
divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Compass
A compass is used to:
✔ Draw arcs
✔ Transfer lengths
✔ Locate points at specified distances
Radius
If an arc is drawn with radius:
$$6\text{ cm}$$
then every point on that arc is:
$$6\text{ cm}$$
from its centre.
Angle Notation
In:
$$\angle ABC$$
the middle letter:
$$B$$
is the vertex.
Related Practice Questions
Q1. What are the diagonals of quadrilateral $$PQRS$$?
Q2. If a compass is opened to $$9\text{ cm}$$, what radius will the arc have?
Q3. What is the vertex of $$\angle XYZ$$?
Q4. Why does a diagonal help in quadrilateral construction?
Q5. What should be done when a completed construction does not match a given length?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. The diagonal $$BD$$ of quadrilateral $$ABCD$$ forms which triangles?
A) $$\triangle ABD$$ and $$\triangle BCD$$
B) $$\triangle ABC$$ and $$\triangle ACD$$
C) $$\triangle ABC$$ only
D) No triangle
Q2. An arc is drawn with centre $$P$$ and radius:
$$7\text{ cm}$$
If $$Q$$ lies on the arc, then:
A) $$PQ=5\text{ cm}$$
B) $$PQ=7\text{ cm}$$
C) $$PQ=14\text{ cm}$$
D) $$PQ=0\text{ cm}$$
Q3. In:
$$\angle XYZ$$
the vertex is:
A) $$X$$
B) $$Y$$
C) $$Z$$
D) None
Q4. Which instrument is mainly used to draw an arc with a fixed radius?
A) Compass
B) Protractor
C) Scale only
D) Set square only
Q5. If a constructed side is significantly different from the given length, what should be done?
A) Check the construction
B) Ignore the difference
C) Change the question
D) Erase the given measurement
Exam Tips
✔ Remember that the middle letter of an angle name is its vertex.
✔ Use the compass carefully when transferring lengths.
✔ A diagonal joins opposite vertices.
✔ Use diagonals to divide quadrilaterals into triangles.
✔ Check every given measurement after construction.
✔ Do not ignore significant measurement errors.
✔ Follow construction steps systematically.
Quick Revision Notes
✔ Diagonal of $$ABCD$$ → $$AC$$ or $$BD$$
✔ $$AC$$ divides $$ABCD$$ into:
$$\triangle ABC$$ and $$\triangle ACD$$
✔ Compass → arcs and length transfer
✔ Protractor → angle measurement
✔ In $$\angle ABC$$ → vertex is $$B$$
✔ Radius determines the fixed distance from the centre.
✔ Construction should satisfy the given measurements.
Common Mistakes Students Make
❌ Reading the first letter as the vertex of an angle.
❌ Using a protractor when a compass is required to transfer a length.
❌ Confusing a side with a diagonal.
❌ Setting the compass to the wrong length.
❌ Not checking the final measurements.
❌ Continuing a construction after identifying a major error.
Key Takeaways
✔ A diagonal can divide a quadrilateral into two triangles.
✔ Compass helps transfer lengths and draw arcs.
✔ The middle letter of an angle represents its vertex.
✔ Every point on an arc is at a fixed distance from its centre.
✔ Accurate measurement is essential for successful construction.
✔ Final constructions should always be verified.
FAQs
Q. What is the vertex of $$\angle ABC$$?
Answer:
The vertex is:
$$B$$
because the middle letter represents the vertex.
Q. What does a compass do in practical geometry?
Answer:
A compass is mainly used to draw circles and arcs and to transfer given lengths accurately.
Q. What is the radius of an arc drawn with a compass opening of $$6\text{ cm}$$?
Answer:
The radius is:
$$6\text{ cm}$$
Q. How does a diagonal help construct a quadrilateral?
Answer:
A diagonal divides the quadrilateral into two triangles, which can be constructed using the available side and diagonal measurements.
Q. Why should a construction be checked after completion?
Answer:
Checking ensures that all given lengths, angles, and other conditions have been satisfied accurately.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on diagonals, arcs, angles, compass usage, and construction verification.
These questions help students strengthen their understanding of practical construction and develop accuracy and logical reasoning for school examinations.
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