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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, angles, diagonals, 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: 5
Difficulty Level: Moderate to Difficult
Based On: NCERT Mathematics
Introduction
Constructing a quadrilateral requires careful use of the information provided in the question. Depending on the data available, students may use sides, angles, diagonals, or combinations of these measurements.
A good construction begins by identifying the measurements that can be used as a starting point. The use of accurate geometrical instruments then helps in completing the figure.
This Practice Set 5 contains 5 fresh MCQs based on NCERT concepts related to construction of quadrilaterals, diagonals, angles, and geometrical reasoning.
What You Will Learn
✔ Selecting a suitable starting measurement
✔ Understanding diagonal-based construction
✔ Applying the properties of quadrilaterals
✔ Using angles and sides in construction
✔ Identifying valid construction information
✔ Checking the accuracy of a geometrical figure
Why This Topic Is Important
Practical Geometry teaches students how mathematical measurements can be converted into accurate geometrical figures. It improves spatial understanding, precision, and logical reasoning.
The ability to identify which measurements are necessary is especially important in construction-based examination 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 quadrilateral has sides of lengths $$5\text{ cm}, 6\text{ cm}, 7\text{ cm}, 8\text{ cm}$$ and a diagonal of length $$9\text{ cm}$$. What can the diagonal be used for during construction?
A) To divide the quadrilateral into two triangles
B) To increase the number of sides
C) To measure the perimeter directly
D) To remove one side
Answer:
A) To divide the quadrilateral into two triangles
Useful Concept
A diagonal joins opposite vertices and divides a quadrilateral into two triangles.
Solution
Suppose the quadrilateral is:
$$ABCD$$
and the given diagonal is:
$$AC=9\text{ cm}$$
The diagonal $$AC$$ divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Thus, the two triangles can be constructed separately using the given measurements.
Therefore, the correct answer is:
A) To divide the quadrilateral into two triangles
Q2. Which of the following is NOT a measurement of a quadrilateral?
A) Side length
B) Angle
C) Diagonal length
D) Colour of the figure
Answer:
D) Colour of the figure
Useful Concept
Geometrical construction depends on mathematical measurements such as lengths and angles, not visual properties such as colour.
Solution
The lengths of sides and diagonals and the measures of angles are mathematical information that can be used during construction.
For example:
$$AB=6\text{ cm}$$
is a side-length measurement.
Similarly:
$$\angle A=80^\circ$$
is an angle measurement.
The colour of a figure has no role in determining its geometrical shape.
Hence, the correct answer is:
D) Colour of the figure
Q3. A student is given $$AB=7\text{ cm}$$ and $$BC=5\text{ cm}$$. If the angle between these two sides is $$60^\circ$$, which point can be located after constructing the two given sides from the common vertex?
A) Point $$C$$
B) Point $$A$$ only
C) No point
D) The diagonal only
Answer:
A) Point $$C$$
Useful Concept
When two sides and the included angle are known, the second endpoint can be located by constructing the given angle and measuring the required side.
Solution
The given measurements are:
$$AB=7\text{ cm}$$
$$BC=5\text{ cm}$$
and:
$$\angle ABC=60^\circ$$
First, draw:
$$AB=7\text{ cm}$$
At point $$B$$, construct:
$$\angle ABC=60^\circ$$
On the constructed ray, mark:
$$BC=5\text{ cm}$$
The endpoint of this segment is point:
$$C$$
Therefore, point $$C$$ can be located using the given information.
Hence, the correct answer is:
A) Point $$C$$
Q4. If a quadrilateral has one pair of opposite sides that are equal, does this information alone always determine a unique quadrilateral?
A) Yes, always
B) No, additional information may be required
C) Yes, because every quadrilateral is a square
D) No quadrilateral can have equal sides
Answer:
B) No, additional information may be required
Useful Concept
A quadrilateral generally requires sufficient independent measurements to determine its shape uniquely.
Solution
Knowing only that one pair of opposite sides is equal does not specify the exact lengths, angles, or positions of all the vertices.
Many different quadrilaterals can satisfy such a condition.
Therefore, additional measurements such as side lengths, angles, or a diagonal may be necessary.
Hence, the correct answer is:
B) No, additional information may be required
Q5. While constructing a quadrilateral, a student draws a side of $$7.5\text{ cm}$$ instead of the required $$7\text{ cm}$$. What is the best action?
A) Continue the construction without correction
B) Correct the side before continuing
C) Change another side to compensate
D) Ignore the difference
Answer:
B) Correct the side before continuing
Useful Concept
Construction should follow the given measurements accurately. An incorrect side length can affect the rest of the construction.
Solution
The required length is:
$$7\text{ cm}$$
but the student has drawn:
$$7.5\text{ cm}$$
The difference is:
$$7.5-7=0.5\text{ cm}$$
Since the given condition is not satisfied, the side should be corrected before continuing the construction.
Changing another side to compensate would not necessarily produce the required quadrilateral.
Therefore, the correct answer is:
B) Correct the side before continuing
Important Concepts
Diagonal
A diagonal joins two opposite vertices of a quadrilateral.
For:
$$ABCD$$
the diagonals are:
$$AC$$
and:
$$BD$$
Two Sides and Included Angle
If two sides and the angle between them are known, they can be used to construct a triangle.
For example:
$$AB=7\text{ cm}$$
$$BC=5\text{ cm}$$
and:
$$\angle ABC=60^\circ$$
provide sufficient information for constructing the triangle.
Accuracy of Lengths
If a length is given as:
$$7\text{ cm}$$
it should be constructed accurately as:
$$7\text{ cm}$$
rather than using an approximate value.
Sufficient Information
A construction requires enough independent measurements to determine the required figure.
Mathematical Measurements
Important construction measurements include:
✔ Side lengths
✔ Angle measures
✔ Diagonal lengths
✔ Other specified geometrical relationships
Related Practice Questions
Q1. If:
$$PQ=6\text{ cm}$$
and:
$$QR=4\text{ cm}$$
with:
$$\angle PQR=90^\circ$$
what information is being provided?
Q2. What is the purpose of a diagonal in a quadrilateral construction?
Q3. Why should a wrong side length be corrected immediately?
Q4. Can colour or shading determine the shape of a quadrilateral?
Q5. Name the two diagonals of quadrilateral:
$$WXYZ$$
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. A diagonal of quadrilateral $$PQRS$$ is:
A) $$PQ$$
B) $$QR$$
C) $$PR$$
D) $$PS$$
Q2. If:
$$AB=8\text{ cm}$$
is required but the student draws:
$$AB=7.8\text{ cm}$$
what should be done?
A) Ignore the error
B) Correct the measurement
C) Change the angle
D) Remove the side
Q3. Which combination is useful for constructing a triangle?
A) Two sides and their included angle
B) Colour and shape
C) Name and perimeter
D) Number of vertices only
Q4. Which of the following is a mathematical measurement?
A) Colour
B) Side length
C) Page size
D) Pencil type
Q5. Why is sufficient information necessary in construction?
A) To determine the required figure accurately
B) To make the figure colourful
C) To increase the number of vertices
D) To avoid using a ruler
Exam Tips
✔ Identify all given measurements before beginning.
✔ Use the diagonal when it is provided as part of the construction data.
✔ Check the exact length of every constructed side.
✔ Construct included angles carefully.
✔ Correct any measurement error before proceeding.
✔ Do not use visual appearance as a substitute for measurement.
✔ Remember that sufficient independent information is necessary for a unique construction.
Quick Revision Notes
✔ A diagonal joins opposite vertices.
✔ A quadrilateral has two diagonals.
✔ A diagonal can divide a quadrilateral into two triangles.
✔ Two sides and their included angle can be used to construct a triangle.
✔ Side lengths should be measured accurately.
✔ Angles should be constructed accurately.
✔ Colour and appearance have no role in determining a geometrical construction.
✔ Sufficient information is required for a unique construction.
Common Mistakes Students Make
❌ Continuing with an incorrect side length.
❌ Treating approximate measurements as exact measurements.
❌ Forgetting to use the given diagonal.
❌ Confusing a side with a diagonal.
❌ Ignoring the included angle.
❌ Assuming that a small measurement error does not matter.
Key Takeaways
✔ Construction depends on accurate mathematical information.
✔ Diagonals can be used to divide quadrilaterals into triangles.
✔ Two sides and their included angle are useful for triangle construction.
✔ Every given length should be constructed accurately.
✔ An incorrect measurement can affect the complete figure.
✔ Sufficient independent information is needed for a unique construction.
FAQs
Q. Why is a diagonal useful when constructing a quadrilateral?
Answer:
A diagonal divides a quadrilateral into two triangles. These triangles can then be constructed using the available measurements.
Q. Why should side lengths be measured accurately?
Answer:
An incorrect side length can change the shape of the final figure and may cause the construction to fail.
Q. What is an included angle?
Answer:
An included angle is the angle formed by two sides that meet at a common vertex.
Q. Does the colour of a figure affect its construction?
Answer:
No. Construction depends on mathematical measurements such as lengths and angles.
Q. What happens if insufficient information is given?
Answer:
The figure may not be uniquely determined, so additional measurements may be necessary.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on diagonal-based construction, included angles, measurement accuracy, and sufficient construction information.
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