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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, sides, 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: 2
Difficulty Level: Moderate
Based On: NCERT Mathematics
Introduction
In Practical Geometry, students learn how to construct geometrical figures when different measurements are provided. A proper construction requires accurate use of a ruler, compass, and protractor.
For constructing a quadrilateral, the information given in the question is very important. Depending on the given measurements, students may need to use sides, angles, diagonals, or combinations of these measurements.
This Practice Set 2 contains 5 fresh MCQs focusing on the basic conditions and methods used in constructing quadrilaterals.
What You Will Learn
✔ Identifying the information needed for construction
✔ Understanding adjacent and opposite sides
✔ Using given angles in construction
✔ Understanding the role of diagonals
✔ Applying ruler and compass constructions
✔ Checking geometrical measurements
Why This Topic Is Important
Construction questions test both mathematical understanding and practical accuracy. Students need to understand how different measurements determine the shape of a quadrilateral.
A strong understanding of these concepts makes it easier to solve construction-based questions 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. Suppose a quadrilateral is to be constructed when four sides and one angle are given. Which type of information is being used to determine the shape of the quadrilateral?
A) Only one side
B) A combination of sides and an angle
C) Only one diagonal
D) Only the perimeter
Answer:
B) A combination of sides and an angle
Useful Concept
A quadrilateral can be constructed when sufficient independent measurements are provided. These may include sides, angles, diagonals, or suitable combinations.
Solution
A quadrilateral has four sides and four angles. To determine its shape, sufficient measurements must be known.
If four sides and one angle are given, the known side lengths together with the angle provide information needed for the construction.
Therefore, this is a case where a combination of sides and an angle is used.
Hence, the correct answer is:
B) A combination of sides and an angle
Q2. In quadrilateral ABCD, which pair represents the opposite sides?
A) $$AB$$ and $$BC$$
B) $$BC$$ and $$CD$$
C) $$AB$$ and $$CD$$
D) $$AD$$ and $$AB$$
Answer:
C) $$AB$$ and $$CD$$
Useful Concept
Opposite sides of a quadrilateral do not share a common vertex.
Solution
Consider quadrilateral:
$$ABCD$$
Its sides are:
$$AB,\ BC,\ CD,\ DA$$
The side $$AB$$ is opposite to $$CD$$ because they do not have a common endpoint.
Similarly, $$BC$$ is opposite to $$AD$$.
Therefore, the correct pair is:
$$AB \text{ and } CD$$
Hence, the correct answer is:
C) $$AB$$ and $$CD$$
Q3. In constructing a quadrilateral, why is it important to use the given angle accurately?
A) Because the angle determines the colour of the figure
B) Because changing the angle can change the shape of the quadrilateral
C) Because an angle determines the number of sides
D) Because angles are used only for decoration
Answer:
B) Because changing the angle can change the shape of the quadrilateral
Useful Concept
Angles determine the direction in which sides are drawn. Therefore, an incorrect angle can produce a different geometrical figure.
Solution
Suppose two sides of a quadrilateral meet at a specified angle.
If that angle is changed, the direction of the second side also changes. As a result, the overall shape of the quadrilateral changes.
Therefore, accurate construction of the given angle is essential.
Hence, the correct answer is:
B) Because changing the angle can change the shape of the quadrilateral
Q4. If a line segment is given as $$AB=6\text{ cm}$$, which instrument is most suitable for drawing the segment with the required length?
A) Compass only
B) Protractor only
C) Ruler
D) Pencil sharpener
Answer:
C) Ruler
Useful Concept
A ruler is used to measure and draw line segments of specified lengths.
Solution
The given measurement is:
$$AB=6\text{ cm}$$
To draw a line segment of exactly $$6\text{ cm}$$, we use a ruler.
The ruler allows us to measure the required length accurately and draw the line segment.
Therefore, the appropriate instrument is:
C) Ruler
Q5. A student has constructed a side of a quadrilateral but the next side must make an angle of $$70^\circ$$ with it. Which instrument should the student use to construct the given angle accurately?
A) Compass
B) Protractor
C) Ruler only
D) Divider only
Answer:
B) Protractor
Useful Concept
A protractor is used to measure and construct angles of specified measures.
Solution
The required angle is:
$$70^\circ$$
Since the student needs to construct an angle of a particular measure, a protractor is the suitable instrument.
The protractor can be used to mark:
$$70^\circ$$
from the given side and then draw the next side through the marked point.
Hence, the correct answer is:
B) Protractor
Important Concepts
Opposite Sides
In quadrilateral:
$$ABCD$$
the pairs of opposite sides are:
$$AB \text{ and } CD$$
and:
$$BC \text{ and } AD$$
Adjacent Sides
Adjacent sides share a common vertex.
For example:
$$AB \text{ and } BC$$
are adjacent sides.
Use of Ruler
A ruler is used to:
✔ Measure lengths
✔ Draw straight line segments
Use of Compass
A compass is used to:
✔ Draw arcs
✔ Draw circles
✔ Transfer lengths
Use of Protractor
A protractor is used to:
✔ Measure angles
✔ Construct angles of specified measures
Importance of Accurate Angles
During construction, an incorrect angle can change the shape and position of the sides. Therefore, angles should be measured carefully.
Related Practice Questions
Q1. In quadrilateral $$PQRS$$, identify the pair of opposite sides.
A) $$PQ$$ and $$QR$$
B) $$PQ$$ and $$RS$$
C) $$QR$$ and $$RS$$
D) $$SP$$ and $$PQ$$
Q2. Which instrument is mainly used to draw a line segment of a specified length?
A) Ruler
B) Compass
C) Protractor
D) Divider
Q3. Which instrument is used to construct an angle of $$45^\circ$$?
A) Ruler
B) Compass
C) Protractor
D) Scale only
Q4. What are adjacent sides?
A) Sides having no common vertex
B) Sides having a common vertex
C) Only diagonal segments
D) Parallel sides only
Q5. If:
$$AB=7\text{ cm}$$
what instrument can be used to draw $$AB$$ accurately?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which pair represents opposite sides of quadrilateral $$WXYZ$$?
A) $$WX$$ and $$XY$$
B) $$XY$$ and $$YZ$$
C) $$WX$$ and $$YZ$$
D) $$ZW$$ and $$WX$$
Q2. Which instrument is used to construct a specified angle?
A) Ruler
B) Protractor
C) Compass
D) Divider
Q3. If a side has to be drawn as:
$$AB=8\text{ cm}$$
which instrument is primarily required?
A) Ruler
B) Protractor
C) Compass
D) Eraser
Q4. Adjacent sides of a quadrilateral:
A) Have a common vertex
B) Never meet
C) Are always equal
D) Are always parallel
Q5. What can happen if an angle is constructed incorrectly?
A) The shape may change
B) The number of sides increases
C) The figure becomes a circle
D) Nothing changes
Exam Tips
✔ Read all the given measurements before beginning a construction.
✔ Use a ruler carefully for specified lengths.
✔ Use a protractor accurately when an angle is given.
✔ Use a compass carefully while transferring lengths.
✔ Distinguish between adjacent and opposite sides.
✔ Keep construction marks visible until the construction is checked.
✔ Label all points correctly.
Quick Revision Notes
✔ A quadrilateral has four sides.
✔ Opposite sides do not have a common vertex.
✔ Adjacent sides have a common vertex.
✔ Ruler is used to draw and measure line segments.
✔ Compass is used to draw arcs and transfer lengths.
✔ Protractor is used to measure and construct angles.
✔ Accurate angles are important for obtaining the required shape.
✔ Construction requires sufficient and appropriate measurements.
Common Mistakes Students Make
❌ Confusing adjacent sides with opposite sides.
❌ Using a ruler instead of a protractor to construct an angle.
❌ Measuring a line segment inaccurately.
❌ Ignoring the exact angle given in the question.
❌ Erasing construction arcs before checking the figure.
❌ Incorrectly labelling the vertices.
Key Takeaways
✔ Practical Geometry involves accurate construction of geometrical figures.
✔ Opposite sides of a quadrilateral do not share a vertex.
✔ Adjacent sides share a common vertex.
✔ A ruler is useful for line segments.
✔ A compass is useful for arcs and transferring lengths.
✔ A protractor is useful for constructing angles.
✔ Correct measurements are essential for an accurate construction.
FAQs
Q. What are opposite sides of a quadrilateral?
Answer:
Opposite sides are sides that do not have a common vertex. In quadrilateral:
$$ABCD$$
the opposite pairs are:
$$AB,CD$$
and:
$$BC,AD$$
Q. What are adjacent sides?
Answer:
Adjacent sides are sides that have a common vertex. For example:
$$AB$$
and:
$$BC$$
are adjacent sides.
Q. Which instrument is used to measure an angle?
Answer:
A protractor is used to measure an angle.
Q. Which instrument is used to draw a line segment of a given length?
Answer:
A ruler is used to draw a line segment of a specified length.
Q. Why are accurate measurements important in construction?
Answer:
Accurate measurements ensure that the constructed figure has the required lengths and angles and matches the conditions given in the question.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ Practice Set 2 provides fresh NCERT-based practice on quadrilateral sides, angles, construction instruments, and measurement concepts.
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