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Practice Class 8 Maths Chapter 4 Practical Geometry MCQ Questions with Answers and Solutions based on NCERT concepts. Test your understanding of quadrilateral construction, diagonals, angles, and geometrical instruments.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 3
Difficulty Level: Moderate
Based On: NCERT Mathematics
Introduction
The construction of a quadrilateral depends on the measurements provided in the question. Students must identify the given information and select an appropriate construction method.
In practical geometry, a quadrilateral may be constructed using different combinations of sides, angles, diagonals, and other measurements. Accurate use of geometrical instruments is essential for obtaining the required figure.
This Practice Set 3 contains 5 fresh MCQs focusing on construction conditions, diagonals, angles, and the relationship between different geometrical measurements.
What You Will Learn
✔ Understanding construction conditions
✔ Using diagonals in quadrilateral construction
✔ Identifying included angles
✔ Applying geometric measurements
✔ Understanding the role of given information
✔ Checking whether a construction is possible
Why This Topic Is Important
Practical Geometry develops precision and logical reasoning. Instead of simply calculating an answer, students learn how a geometrical figure can actually be constructed from given information.
Understanding the construction conditions also helps students avoid incomplete or incorrect constructions.
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 is to be constructed using the lengths of its four sides and one diagonal. What should be done first if the diagonal is given as $$AC=5\text{ cm}$$?
A) Draw a circle only
B) Draw the diagonal $$AC$$ of length $$5\text{ cm}$$
C) Measure all four angles
D) Draw all four sides at once
Answer:
B) Draw the diagonal $$AC$$ of length $$5\text{ cm}$$
Useful Concept
When a diagonal is given along with the side lengths, the diagonal can be used as the base for constructing the two triangles forming the quadrilateral.
Solution
The given diagonal is:
$$AC=5\text{ cm}$$
The first step is to draw the line segment:
$$AC=5\text{ cm}$$
This diagonal divides the quadrilateral into two triangles:
$$\triangle ABC$$
and:
$$\triangle ACD$$
The remaining sides can then be constructed using the given lengths.
Therefore, the correct first step is:
B) Draw the diagonal $$AC$$ of length $$5\text{ cm}$$
Q2. In a quadrilateral, an angle formed by two sides that meet at the same vertex is called:
A) Opposite angle
B) Included angle
C) Exterior angle only
D) Diagonal angle
Answer:
B) Included angle
Useful Concept
The angle between two sides meeting at a common vertex is called the included angle between those sides.
Solution
Suppose two sides:
$$AB$$
and:
$$BC$$
meet at vertex:
$$B$$
The angle:
$$\angle ABC$$
is formed by these two sides.
Therefore, it is the angle included between:
$$AB$$
and:
$$BC$$
Hence, the correct answer is:
B) Included angle
Q3. A student has four sides of a quadrilateral but no other measurement. Why may these four side lengths alone be insufficient to determine a unique quadrilateral?
A) A quadrilateral cannot have four sides
B) The shape can change while the side lengths remain the same
C) A ruler cannot measure four sides
D) Every quadrilateral must be a square
Answer:
B) The shape can change while the side lengths remain the same
Useful Concept
Four side lengths alone do not always fix the angles and shape of a quadrilateral uniquely.
Solution
Consider a quadrilateral with four fixed side lengths.
The sides can sometimes be arranged in different ways while keeping their lengths unchanged. This can produce quadrilaterals with different angles and shapes.
Therefore, additional information such as a diagonal or an angle may be needed to determine the quadrilateral uniquely.
Hence, the correct answer is:
B) The shape can change while the side lengths remain the same
Q4. Which of the following pairs of measurements can provide useful information for constructing a quadrilateral?
A) Four sides and one diagonal
B) Only the name of the quadrilateral
C) Only the colour of the figure
D) Only the number of vertices
Answer:
A) Four sides and one diagonal
Useful Concept
A sufficient set of geometrical measurements is required to determine the shape of a quadrilateral.
Solution
The name, colour, or number of vertices does not provide enough information to construct a particular quadrilateral.
However, four side lengths together with one diagonal provide useful measurements. The diagonal divides the quadrilateral into two triangles, allowing the construction to be carried out systematically.
Therefore, the correct answer is:
A) Four sides and one diagonal
Q5. Suppose a construction requires an angle of $$110^\circ$$. Which of the following is the most appropriate way to ensure that the angle is accurate?
A) Draw it by guessing
B) Use a protractor
C) Use a ruler without measurement
D) Draw a random arc
Answer:
B) Use a protractor
Useful Concept
A protractor helps in measuring and constructing an angle of a specified degree.
Solution
The required angle is:
$$110^\circ$$
Since the exact measure of the angle is given, it should not be drawn by estimation.
A protractor can be used to locate the:
$$110^\circ$$
mark accurately.
Therefore, the correct answer is:
B) Use a protractor
Important Concepts
Diagonal-Based Construction
A diagonal can divide a quadrilateral into two triangles.
For quadrilateral:
$$ABCD$$
diagonal:
$$AC$$
creates:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Included Angle
The angle formed by two sides meeting at a common vertex is the included angle between those sides.
For example:
$$\angle ABC$$
is the included angle between:
$$AB$$
and:
$$BC$$
Four Sides Are Not Always Sufficient
Knowing only the four side lengths may not always determine one unique quadrilateral.
Additional information such as a diagonal or an angle can be required.
Accuracy in Construction
Construction should be performed using accurate measurements rather than estimation.
Role of Protractor
A protractor is useful when an exact angle such as:
$$60^\circ,\ 90^\circ,\ 110^\circ$$
is given.
Related Practice Questions
Q1. What does a diagonal do to a quadrilateral?
A) Divides it into two triangles
B) Divides it into two circles
C) Removes one side
D) Creates a pentagon
Q2. In:
$$\angle PQR$$
which point represents the vertex?
A) $$P$$
B) $$Q$$
C) $$R$$
D) None
Q3. Why may an additional measurement be required with four given sides?
A) To determine the shape more precisely
B) To increase the number of sides
C) To change the name of the figure
D) To remove the diagonal
Q4. Which instrument is appropriate for constructing:
$$75^\circ$$
A) Protractor
B) Ruler only
C) Compass only
D) Pencil
Q5. If:
$$BD=6\text{ cm}$$
is given as a diagonal, what can it help us construct?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. A diagonal divides a quadrilateral into:
A) One triangle
B) Two triangles
C) Three triangles
D) Four triangles
Q2. Which measurement can help determine the shape of a quadrilateral along with its four sides?
A) A diagonal
B) Its colour
C) Its name
D) Its perimeter only
Q3. In:
$$\angle XYZ$$
the vertex is:
A) $$X$$
B) $$Y$$
C) $$Z$$
D) $$XZ$$
Q4. An angle of:
$$85^\circ$$
can be constructed accurately using:
A) Protractor
B) Ruler only
C) Eraser
D) Pencil only
Q5. Why should a construction not be based on guessing?
A) It may produce an inaccurate figure
B) It changes the number of vertices
C) It removes the sides
D) It always produces a circle
Exam Tips
✔ Read every given measurement carefully.
✔ Identify whether a side, angle, or diagonal is provided.
✔ Use a diagonal as a base when the construction method requires it.
✔ Do not estimate an angle when its exact measure is given.
✔ Use the protractor for accurate angle measurement.
✔ Remember that four side lengths alone may not always determine a unique quadrilateral.
✔ Keep construction steps neat and properly labelled.
Quick Revision Notes
✔ A diagonal joins two opposite vertices.
✔ A diagonal divides a quadrilateral into two triangles.
✔ Four side lengths may not always determine a unique quadrilateral.
✔ Additional information can include an angle or a diagonal.
✔ An included angle is formed by two sides meeting at a common vertex.
✔ A protractor is used for accurate angle measurement.
✔ A ruler is used for drawing specified line segments.
✔ Accurate construction requires careful measurement.
Common Mistakes Students Make
❌ Assuming that four side lengths always determine one unique quadrilateral.
❌ Forgetting the role of a diagonal in construction.
❌ Measuring an angle from the wrong baseline.
❌ Reading the incorrect scale of the protractor.
❌ Drawing angles by estimation when an exact measurement is given.
❌ Failing to label the vertices correctly.
Key Takeaways
✔ A quadrilateral can be constructed using sufficient independent measurements.
✔ A diagonal is useful because it divides a quadrilateral into two triangles.
✔ Four sides alone may not always determine a unique quadrilateral.
✔ Included angles are formed by two sides meeting at a common vertex.
✔ A protractor provides accurate angle measurements.
✔ Careful measurement is essential in practical geometry.
FAQs
Q. Why can four sides alone be insufficient to construct a unique quadrilateral?
Answer:
Four side lengths may allow different shapes with different angles. Therefore, an additional measurement such as a diagonal or angle may be required.
Q. What is an included angle?
Answer:
An included angle is the angle formed by two sides that meet at a common vertex.
Q. How does a diagonal help in constructing a quadrilateral?
Answer:
A diagonal divides the quadrilateral into two triangles. These triangles can then be constructed using the available measurements.
Q. Which instrument is used to construct a given angle?
Answer:
A protractor is used to measure and construct an angle of a specified measure.
Q. Why is accuracy important in practical geometry?
Answer:
Accurate measurements ensure that the constructed figure satisfies all the conditions given in the question.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based questions on diagonal-based construction, included angles, construction conditions, and accurate measurement.
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