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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: 15
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Practical Geometry deals with the construction of geometrical figures using specific measurements. In the case of quadrilaterals, a figure can be constructed when sufficient information about its sides, angles, and diagonals is provided.
The important skill is to identify the given measurements and use them in the correct sequence. A diagonal can divide a quadrilateral into two triangles, while a compass and protractor help transfer lengths and construct angles accurately.
This Practice Set 15 contains 5 fresh and challenging MCQs covering different construction conditions, diagonals, angles, compass use, and verification.
What You Will Learn
✔ Identifying sufficient information for construction
✔ Understanding different quadrilateral construction cases
✔ Using diagonals to form triangles
✔ Constructing given angles
✔ Using a compass to transfer lengths
✔ Checking the accuracy of constructions
Why This Topic Is Important
Practical Geometry develops accuracy, visualisation, and logical reasoning. It teaches students how a geometrical figure can be constructed from a suitable set of measurements rather than simply drawing an approximate figure.
These concepts are particularly useful in NCERT-based 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. Which of the following sets of measurements is sufficient to construct a quadrilateral?
A) Four sides and one diagonal
B) One side only
C) Two sides only
D) One angle only
Answer:
A) Four sides and one diagonal
Useful Concept
A quadrilateral can be constructed when its four sides and one diagonal are known.
Solution
Suppose quadrilateral $$ABCD$$ is given.
If the following measurements are known:
$$AB,\ BC,\ CD,\ DA$$
and one diagonal:
$$AC$$
then the quadrilateral can be constructed by first constructing the diagonal and then constructing the two triangles on either side of it.
The diagonal divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Therefore, four sides and one diagonal provide sufficient information.
Hence, the correct answer is:
A) Four sides and one diagonal
Q2. A quadrilateral $$ABCD$$ is to be constructed when three sides and two diagonals are known. If the known measurements are $$AB$$, $$BC$$, $$CD$$, $$AC$$, and $$BD$$, which side is not directly given?
A) $$AB$$
B) $$BC$$
C) $$CD$$
D) $$AD$$
Answer:
D) $$AD$$
Useful Concept
In construction problems, carefully identify which sides and diagonals are actually provided.
Solution
The given sides are:
$$AB$$
$$BC$$
and:
$$CD$$
The given diagonals are:
$$AC$$
and:
$$BD$$
The remaining side is:
$$AD$$
Therefore, $$AD$$ is not directly given.
However, the given three sides and two diagonals provide sufficient information for constructing the quadrilateral through the appropriate construction method.
Hence, the correct answer is:
D) $$AD$$
Q3. A quadrilateral has two adjacent sides of lengths $$5\text{ cm}$$ and $$6\text{ cm}$$. Three angles are given as:
$$70^\circ,\ 80^\circ,\ 110^\circ$$
Which type of information is being used for its construction?
A) Two adjacent sides and three angles
B) Four sides and one diagonal
C) Three sides and two diagonals
D) One side and one diagonal
Answer:
A) Two adjacent sides and three angles
Useful Concept
A quadrilateral can be constructed when two adjacent sides and three angles are known.
Solution
The given side information consists of two adjacent sides:
$$5\text{ cm}$$
and:
$$6\text{ cm}$$
The three angle measurements are:
$$70^\circ,\ 80^\circ,\ 110^\circ$$
Therefore, the construction data consists of:
Two adjacent sides + three angles
The fourth angle is not required to be separately given because the necessary construction information is already available.
Hence, the correct answer is:
A) Two adjacent sides and three angles
Q4. During a construction, a student needs to reproduce a segment of length $$7.5\text{ cm}$$ at another location. Which method is most appropriate?
A) Use a compass to transfer the length
B) Estimate the length visually
C) Draw an arbitrary segment
D) Use an eraser to mark the distance
Answer:
A) Use a compass to transfer the length
Useful Concept
A compass can transfer a given length from one position to another without changing its measure.
Solution
The required length is:
$$7.5\text{ cm}$$
The compass can be opened so that its tips coincide with the endpoints of the original segment.
Without changing the compass opening, the same distance can then be marked at another location.
This ensures that the transferred segment has the same length:
$$7.5\text{ cm}$$
Hence, the correct answer is:
A) Use a compass to transfer the length
Q5. After constructing a quadrilateral, a student finds that one of the given angles does not match the required measurement. What should be done first?
A) Check the construction steps and measurements
B) Ignore the difference
C) Change the given angle
D) Change the name of the quadrilateral
Answer:
A) Check the construction steps and measurements
Useful Concept
A geometrical construction is correct only when all the conditions given in the problem are satisfied.
Solution
Suppose the required angle is:
$$85^\circ$$
but the constructed angle is different.
The student should first check:
✔ The protractor placement
✔ The initial ray
✔ The angle marking
✔ The construction sequence
✔ The given measurements
The original condition should not simply be changed.
Therefore, the construction should be checked and corrected.
Hence, the correct answer is:
A) Check the construction steps and measurements
Important Concepts
Four Sides and One Diagonal
A quadrilateral can be constructed when its four sides and one diagonal are known.
For quadrilateral:
$$ABCD$$
the information may be:
$$AB,\ BC,\ CD,\ DA$$
and:
$$AC$$
The diagonal divides the quadrilateral into two triangles.
Three Sides and Two Diagonals
A quadrilateral can also be constructed when three sides and both diagonals are given.
For example:
$$AB,\ BC,\ CD,\ AC,\ BD$$
provide three sides and two diagonals.
Two Adjacent Sides and Three Angles
A quadrilateral can be constructed when two adjacent sides and three angles are known.
For example:
$$AB,\ BC$$
along with:
$$\angle A,\ \angle B,\ \angle C$$
provide the necessary information.
Compass
A compass is used to:
✔ Draw arcs
✔ Draw circles
✔ Transfer lengths
✔ Locate points at specified distances
Protractor
A protractor is mainly used to:
✔ Measure angles
✔ Construct angles
Verification
After completing a construction, check:
✔ Side lengths
✔ Angles
✔ Diagonals
✔ Position of vertices
Related Practice Questions
Q1. What information is sufficient for constructing a quadrilateral using the diagonal method?
Q2. Which two diagonals does quadrilateral $$PQRS$$ have?
Q3. What is the role of a compass in construction?
Q4. What information is represented by two adjacent sides and three angles?
Q5. Why should a completed construction be verified?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which set can be used to construct a quadrilateral?
A) Four sides and one diagonal
B) One side only
C) One angle only
D) Two vertices only
Q2. Which of the following is a diagonal of quadrilateral $$ABCD$$?
A) $$AB$$
B) $$BC$$
C) $$AC$$
D) $$CD$$
Q3. Which instrument is mainly used for transferring a length?
A) Compass
B) Protractor
C) Eraser
D) Pencil sharpener
Q4. Which information represents a valid construction condition?
A) Two adjacent sides and three angles
B) One side and no other information
C) One angle only
D) One vertex only
Q5. If a constructed angle differs from the given angle, what should be done?
A) Check and correct the construction
B) Ignore the difference
C) Change the question
D) Remove the angle
Exam Tips
✔ Read all the given measurements before beginning construction.
✔ Identify whether the problem provides sides, angles, or diagonals.
✔ Remember the different conditions used for constructing quadrilaterals.
✔ Use the compass carefully when transferring lengths.
✔ Use the protractor accurately for angle construction.
✔ Keep the compass opening unchanged while transferring a fixed length.
✔ Always verify the final figure against the given conditions.
Quick Revision Notes
✔ Four sides + one diagonal → quadrilateral construction.
✔ Three sides + two diagonals → quadrilateral construction.
✔ Two adjacent sides + three angles → quadrilateral construction.
✔ Diagonal → joins opposite vertices.
✔ Compass → transfers lengths and draws arcs.
✔ Protractor → measures and constructs angles.
✔ Verification → confirms that all given conditions are satisfied.
Common Mistakes Students Make
❌ Starting construction without identifying the given measurements.
❌ Confusing sides with diagonals.
❌ Constructing an angle at the wrong vertex.
❌ Changing the compass opening while transferring a length.
❌ Estimating an angle instead of measuring it accurately.
❌ Ignoring an incorrect measurement after construction.
❌ Changing the given data instead of correcting the construction.
Key Takeaways
✔ Practical Geometry requires accurate measurements and systematic construction.
✔ Four sides and one diagonal are sufficient to construct a quadrilateral.
✔ Three sides and two diagonals can also determine a quadrilateral.
✔ Two adjacent sides and three angles provide another construction condition.
✔ Compass and protractor have different roles in construction.
✔ Every completed construction should be checked carefully.
FAQs
Q. What information is required to construct a quadrilateral using four sides and one diagonal?
Answer:
The four side lengths and one diagonal are required.
For example:
$$AB,\ BC,\ CD,\ DA$$
and:
$$AC$$
Q. What are the diagonals of quadrilateral $$ABCD$$?
Answer:
The diagonals are:
$$AC$$
and:
$$BD$$
because they join opposite vertices.
Q. Which instrument is used to transfer a given length?
Answer:
A compass is used to transfer a given length accurately from one location to another.
Q. Can a quadrilateral be constructed using two adjacent sides and three angles?
Answer:
Yes. Two adjacent sides and three angles provide sufficient information for constructing a quadrilateral.
Q. Why is verification necessary after construction?
Answer:
Verification ensures that the constructed figure satisfies all the given side lengths, angles, diagonals, and other conditions.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on quadrilateral construction conditions, diagonals, angles, compass usage, and verification.
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