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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 quadrilaterals, constructions, diagonals, angles, and geometric constructions.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 1
Difficulty Level: Moderate
Based On: NCERT Mathematics
Introduction
Practical Geometry is an important chapter in Class 8 Mathematics. It deals with the construction of geometrical figures using mathematical instruments such as a ruler, compass, and protractor.
In this chapter, students learn how to construct quadrilaterals when different combinations of measurements are given. The construction process requires careful observation, accurate measurement, and proper use of geometrical instruments.
This Practice Set 1 contains 5 fresh MCQs based on fundamental NCERT concepts of practical geometry and quadrilateral construction.
What You Will Learn
✔ Basic ideas related to geometrical constructions
✔ Conditions required for constructing a quadrilateral
✔ Use of ruler, compass, and protractor
✔ Properties of diagonals and angles
✔ Identification of measurements required for construction
✔ Application of construction concepts
Why This Topic Is Important
Practical Geometry develops students’ accuracy and logical thinking. It helps students understand how geometrical figures can be constructed when specific measurements are known.
These concepts are useful for solving construction-based questions in school examinations and for developing a strong foundation in geometry.
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 instruments is mainly used to draw arcs of a given radius during a geometrical construction?
A) Ruler
B) Compass
C) Protractor
D) Set square
Answer:
B) Compass
Useful Concept
A compass is used to draw circles and arcs with a specified radius. It is also useful for transferring a given length from one location to another.
Solution
During geometrical constructions, different instruments have different purposes.
A ruler is generally used to draw line segments.
A protractor is used to measure or construct angles.
A compass is used to draw arcs and circles with a particular radius.
Therefore, the correct answer is:
B) Compass
Q2. A quadrilateral can be constructed uniquely when which of the following sets of measurements is known?
A) Four sides only
B) Three sides only
C) Four sides and one diagonal
D) Two sides only
Answer:
C) Four sides and one diagonal
Useful Concept
A quadrilateral generally requires sufficient independent measurements to determine its shape uniquely. Four sides alone do not always determine a unique quadrilateral.
Solution
A quadrilateral has four sides, but knowing only the four side lengths does not necessarily fix its shape.
If one diagonal is also given, the quadrilateral can be divided into two triangles.
For example, if the four sides and one diagonal are known, two triangles can be constructed using the given measurements.
Therefore, the quadrilateral can be constructed uniquely under the required construction conditions.
Hence, the correct answer is:
C) Four sides and one diagonal
Q3. If one diagonal and the three sides of a quadrilateral are given, into how many triangles can the quadrilateral be divided by that diagonal?
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2
Useful Concept
A diagonal of a quadrilateral joins two opposite vertices and divides the quadrilateral into two triangles.
Solution
Consider a quadrilateral:
$$ABCD$$
Its diagonal:
$$AC$$
joins the opposite vertices.
The diagonal divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Thus, the quadrilateral is divided into two triangles.
Hence, the correct answer is:
B) 2
Q4. To construct a quadrilateral when four sides and one diagonal are given, which geometrical construction is especially useful?
A) Constructing two triangles
B) Constructing only one angle
C) Drawing only a circle
D) Measuring only the perimeter
Answer:
A) Constructing two triangles
Useful Concept
A diagonal divides a quadrilateral into two triangles. Therefore, the construction can be completed by constructing the two triangles separately.
Solution
Suppose the quadrilateral is:
$$ABCD$$
and diagonal:
$$AC$$
is given.
The diagonal divides the quadrilateral into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
The first triangle can be constructed using its given side lengths. Then the second triangle can be constructed on the other side of the diagonal.
Thus, construction of the quadrilateral is based on constructing two triangles.
Hence, the correct answer is:
A) Constructing two triangles
Q5. Which measurement is represented by the line segment joining two opposite vertices of a quadrilateral?
A) Side
B) Angle
C) Diagonal
D) Perpendicular
Answer:
C) Diagonal
Useful Concept
A diagonal of a polygon joins two non-adjacent or opposite vertices.
Solution
Consider a quadrilateral:
$$ABCD$$
Its sides are:
$$AB,\ BC,\ CD,\ DA$$
The line segments joining opposite vertices are:
$$AC$$
and:
$$BD$$
These line segments are called diagonals.
Therefore, a line segment joining two opposite vertices of a quadrilateral is called a diagonal.
Hence, the correct answer is:
C) Diagonal
Important Concepts
Quadrilateral
A quadrilateral is a closed geometrical figure having four sides, four vertices, and four angles.
Diagonal
A diagonal joins two opposite vertices of a quadrilateral.
For quadrilateral:
$$ABCD$$
the diagonals are:
$$AC$$
and:
$$BD$$
Construction Instruments
A ruler is used to draw line segments.
A compass is used to draw arcs and circles and to transfer lengths.
A protractor is used to measure and construct angles.
Diagonal and Triangles
A diagonal of a quadrilateral divides it into two triangles.
For example:
$$ABCD \rightarrow \triangle ABC+\triangle ACD$$
Construction of Quadrilaterals
A quadrilateral can be constructed when sufficient independent measurements are provided, such as appropriate combinations of sides, angles, diagonals, or other required measurements.
Related Practice Questions
Q1. What instrument is used to measure an angle?
A) Compass
B) Protractor
C) Ruler
D) Divider
Q2. How many diagonals does a quadrilateral have?
A) 1
B) 2
C) 3
D) 4
Q3. What does a diagonal of a quadrilateral divide it into?
A) Two triangles
B) Two circles
C) Four triangles
D) Three rectangles
Q4. Name the diagonals of quadrilateral:
$$PQRS$$
Q5. Which instrument is used to transfer a given length during construction?
A) Compass
B) Protractor
C) Ruler
D) Graph paper
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. How many sides does a quadrilateral have?
A) 3
B) 4
C) 5
D) 6
Q2. How many diagonals does a quadrilateral have?
A) 1
B) 2
C) 3
D) 4
Q3. Which instrument is used to draw an arc with a fixed radius?
A) Ruler
B) Compass
C) Protractor
D) Set square
Q4. A diagonal of a quadrilateral divides it into:
A) One triangle
B) Two triangles
C) Three triangles
D) Four triangles
Q5. Which of the following is a diagonal of quadrilateral:
$$ABCD$$
A) $$AB$$
B) $$BC$$
C) $$AC$$
D) $$CD$$
Exam Tips
✔ Learn the correct use of each geometrical instrument.
✔ Remember that a diagonal joins opposite vertices.
✔ Check whether the given measurements are sufficient before starting a construction.
✔ Draw construction lines lightly and clearly.
✔ Use the compass carefully while transferring lengths.
✔ Use the ruler accurately for measuring and drawing line segments.
✔ Label all vertices correctly after completing the construction.
Quick Revision Notes
✔ A quadrilateral has four sides.
✔ A quadrilateral has four vertices.
✔ A quadrilateral has two diagonals.
✔ The diagonals of:
$$ABCD$$
are:
$$AC$$
and:
$$BD$$
✔ A diagonal divides a quadrilateral into two triangles.
✔ A compass is used to draw arcs and circles.
✔ A ruler is used to draw line segments.
✔ A protractor is used to measure and construct angles.
✔ Practical Geometry requires accurate measurement and careful construction.
Common Mistakes Students Make
❌ Confusing a diagonal with a side of a quadrilateral.
❌ Using a protractor instead of a compass to transfer a length.
❌ Forgetting to check whether sufficient measurements are provided.
❌ Drawing construction arcs inaccurately.
❌ Mislabeling vertices during construction.
❌ Not maintaining the given measurements while constructing the figure.
Key Takeaways
✔ Practical Geometry deals with the construction of geometrical figures.
✔ A quadrilateral has four sides and two diagonals.
✔ A diagonal joins two opposite vertices.
✔ A diagonal divides a quadrilateral into two triangles.
✔ A compass helps in drawing arcs and transferring lengths.
✔ A ruler is used to draw line segments.
✔ A protractor is used to measure and construct angles.
✔ Accurate measurements are essential for geometrical constructions.
FAQs
Q. What is a quadrilateral?
Answer:
A quadrilateral is a closed geometrical figure having four sides, four vertices, and four angles.
Q. What is a diagonal?
Answer:
A diagonal is a line segment joining two opposite vertices of a polygon.
Q. How many diagonals does a quadrilateral have?
Answer:
A quadrilateral has two diagonals.
For quadrilateral:
$$ABCD$$
the diagonals are:
$$AC$$
and:
$$BD$$
Q. Which instrument is used to draw arcs?
Answer:
A compass is used to draw arcs and circles of specified radii.
Q. Why is a diagonal useful in constructing a quadrilateral?
Answer:
A diagonal divides a quadrilateral into two triangles. These triangles can then be constructed using the given measurements.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on geometrical instruments, quadrilaterals, diagonals, and basic construction concepts.
Regular practice of these questions helps students improve their understanding of geometrical constructions and prepares them for NCERT-based school examinations.
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