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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 MCQs 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: 11
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Practical Geometry requires careful interpretation of the information given in a construction problem. Once the available measurements are identified, students must select an appropriate sequence of construction steps.
A quadrilateral may be constructed using combinations of sides, angles, and diagonals. Accurate use of a ruler, compass, and protractor is essential for obtaining the required figure.
This Practice Set 11 contains 5 fresh MCQs focusing on construction reasoning, diagonals, angles, and verification of geometrical figures.
What You Will Learn
✔ Identifying the correct construction method
✔ Understanding the role of diagonals
✔ Using angles and side lengths together
✔ Applying compass and protractor correctly
✔ Locating unknown vertices
✔ Verifying geometrical constructions
Why This Topic Is Important
Practical Geometry develops precision and logical reasoning. Students learn that a geometrical figure cannot always be constructed from incomplete information.
Understanding which measurements are necessary makes construction questions easier and improves accuracy in 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 when $$AB$$, $$BC$$, $$CD$$, and diagonal $$AC$$ are known. Which additional measurement is required to complete the construction?
A) Length of $$AD$$
B) Colour of the quadrilateral
C) Length of $$AB$$ again
D) Number of vertices
Answer:
A) Length of $$AD$$
Useful Concept
Four sides and one diagonal provide sufficient information for constructing a quadrilateral.
Solution
The known measurements are:
$$AB$$
$$BC$$
$$CD$$
and:
$$AC$$
The side:
$$AD$$
is still unknown.
Therefore, to use the standard construction method of four sides and one diagonal, the length of:
$$AD$$
must also be known.
Once all four sides and diagonal $$AC$$ are available, the quadrilateral can be constructed by forming two triangles around the diagonal.
Hence, the correct answer is:
A) Length of $$AD$$
Q2. In a construction, a student draws a line segment $$PQ=9\text{ cm}$$. An arc with centre $$P$$ has radius $$5\text{ cm}$$. What does the arc represent?
A) Points that are $$5\text{ cm}$$ from $$P$$
B) Points that are $$9\text{ cm}$$ from $$P$$
C) Points that are $$14\text{ cm}$$ from $$P$$
D) Points that are $$4\text{ cm}$$ from $$P$$
Answer:
A) Points that are $$5\text{ cm}$$ from $$P$$
Useful Concept
An arc drawn with a particular centre and radius represents points at that fixed distance from the centre.
Solution
The centre of the arc is:
$$P$$
and its radius is:
$$5\text{ cm}$$
Therefore, every point on the arc is at a distance:
$$5\text{ cm}$$
from $$P$$.
The length:
$$PQ=9\text{ cm}$$
does not change the radius of this particular arc.
Hence, the correct answer is:
A) Points that are $$5\text{ cm}$$ from $$P$$
Q3. During the construction of a quadrilateral, the required angle is $$110^\circ$$, but a student constructs $$100^\circ$$. What is the most appropriate action?
A) Continue because the difference is small
B) Correct the angle before continuing
C) Change the side length
D) Ignore the given angle
Answer:
B) Correct the angle before continuing
Useful Concept
Construction must satisfy the exact measurements specified in the question.
Solution
The required angle is:
$$110^\circ$$
but the constructed angle is:
$$100^\circ$$
The difference is:
$$110^\circ-100^\circ=10^\circ$$
The constructed figure therefore does not satisfy the given condition.
The angle should be corrected to:
$$110^\circ$$
before continuing the construction.
Hence, the correct answer is:
B) Correct the angle before continuing
Q4. A diagonal $$AC$$ divides quadrilateral $$ABCD$$ into two triangles. Which two triangles are formed?
A) $$\triangle ABC$$ and $$\triangle ACD$$
B) $$\triangle ABD$$ and $$\triangle BCD$$
C) $$\triangle ABC$$ and $$\triangle BCD$$
D) $$\triangle ACD$$ and $$\triangle ABD$$
Answer:
A) $$\triangle ABC$$ and $$\triangle ACD$$
Useful Concept
A diagonal joins opposite vertices and divides the quadrilateral into two triangles.
Solution
Consider quadrilateral:
$$ABCD$$
The diagonal is:
$$AC$$
The first triangle formed is:
$$\triangle ABC$$
The second triangle formed is:
$$\triangle ACD$$
Together, these two triangles make the original quadrilateral.
Therefore, the correct answer is:
A) $$\triangle ABC$$ and $$\triangle ACD$$
Q5. A student is given the following information:
$$AB=6\text{ cm}$$
$$BC=5\text{ cm}$$
$$CD=7\text{ cm}$$
$$DA=4\text{ cm}$$
and:
$$AC=8\text{ cm}$$
Which construction principle is being used?
A) Four sides and one diagonal
B) Two sides and one angle
C) Four angles only
D) One side and two diagonals
Answer:
A) Four sides and one diagonal
Useful Concept
Four side lengths together with one diagonal provide sufficient information for constructing a unique quadrilateral.
Solution
The four given sides are:
$$AB=6\text{ cm}$$
$$BC=5\text{ cm}$$
$$CD=7\text{ cm}$$
and:
$$DA=4\text{ cm}$$
The additional measurement is the diagonal:
$$AC=8\text{ cm}$$
Therefore, the given information consists of:
Four sides + one diagonal
This is a standard construction condition for a quadrilateral.
Hence, the correct answer is:
A) Four sides and one diagonal
Important Concepts
Four Sides and One Diagonal
A quadrilateral can be constructed when all four side lengths and one diagonal are known.
For:
$$ABCD$$
the information may be:
$$AB,\ BC,\ CD,\ DA$$
and:
$$AC$$
Diagonal Construction
A diagonal divides a quadrilateral into two triangles.
For diagonal:
$$AC$$
the triangles are:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Arc and Radius
An arc with centre $$P$$ and radius:
$$r$$
represents points at distance:
$$r$$
from $$P$$.
Accuracy of Angles
If the required angle is:
$$110^\circ$$
constructing:
$$100^\circ$$
does not satisfy the condition.
Verification
Every given:
✔ Side
✔ Angle
✔ Diagonal
✔ Distance
should be checked after construction.
Related Practice Questions
Q1. What information is needed along with three sides to use the four-sides-and-diagonal construction method?
Q2. If an arc has centre $$O$$ and radius $$6\text{ cm}$$, what is the distance of each point on the arc from $$O$$?
Q3. What triangles are formed by diagonal $$BD$$ in quadrilateral $$ABCD$$?
Q4. Why must a wrongly constructed angle be corrected?
Q5. What are the four side lengths of quadrilateral $$PQRS$$?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Four sides and which additional measurement can be used to construct a quadrilateral?
A) One diagonal
B) One colour
C) One page
D) One pencil
Q2. An arc with radius:
$$8\text{ cm}$$
contains points that are:
A) $$4\text{ cm}$$ from its centre
B) $$8\text{ cm}$$ from its centre
C) $$16\text{ cm}$$ from its centre
D) At random distances
Q3. Diagonal $$BD$$ of quadrilateral $$ABCD$$ forms:
A) $$\triangle ABD$$ and $$\triangle BCD$$
B) $$\triangle ABC$$ and $$\triangle ACD$$
C) $$\triangle ABC$$ only
D) No triangles
Q4. If the required angle is:
$$75^\circ$$
but the student constructs:
$$70^\circ$$
what should be done?
A) Correct the angle
B) Ignore it
C) Change the diagonal
D) Continue without checking
Q5. Which information represents a standard quadrilateral construction condition?
A) Four sides and one diagonal
B) One side and one angle
C) Two angles only
D) One diagonal only
Exam Tips
✔ Identify the exact construction data before beginning.
✔ Remember the four-sides-and-one-diagonal condition.
✔ Use a diagonal to divide a quadrilateral into two triangles.
✔ Keep compass openings accurate.
✔ Construct angles using the exact given measure.
✔ Do not continue with an incorrect measurement.
✔ Verify all conditions after completing the construction.
Quick Revision Notes
✔ Four sides + one diagonal → sufficient for quadrilateral construction.
✔ Diagonal $$AC$$ divides $$ABCD$$ into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
✔ An arc of radius $$r$$ contains points at distance $$r$$ from its centre.
✔ Given angles must be constructed accurately.
✔ Construction errors should be corrected immediately.
Common Mistakes Students Make
❌ Forgetting one of the four side lengths.
❌ Confusing a diagonal with a side.
❌ Using an incorrect compass radius.
❌ Constructing an approximate angle instead of the given angle.
❌ Continuing after noticing a measurement error.
❌ Failing to verify the final quadrilateral.
Key Takeaways
✔ Four sides and one diagonal provide sufficient information for constructing a quadrilateral.
✔ A diagonal divides a quadrilateral into two triangles.
✔ Arcs represent fixed distances from their centres.
✔ Exact angles are important in construction.
✔ Every construction should be verified carefully.
FAQs
Q. What is required to construct a quadrilateral using the four-sides-and-diagonal method?
Answer:
The four side lengths and one diagonal are required.
Q. What does an arc of radius $$5\text{ cm}$$ represent?
Answer:
It represents points that are exactly:
$$5\text{ cm}$$
from its centre.
Q. What happens when diagonal $$AC$$ is drawn in quadrilateral $$ABCD$$?
Answer:
It divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Q. Why should construction errors be corrected immediately?
Answer:
An incorrect length or angle can affect the position of later points and may result in an incorrect final figure.
Q. Why is verification important?
Answer:
Verification ensures that the constructed figure satisfies all the measurements and conditions given in the question.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on four sides and one diagonal, arcs, angles, and the correct construction sequence.
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