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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, diagonals, angles, 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: 14
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Practical Geometry teaches students how to construct geometrical figures when sufficient measurements are provided. In quadrilateral construction, students must understand the relationship between sides, angles, and diagonals and follow a logical sequence of construction.
A successful construction requires accurate measurements and correct use of geometrical instruments. Students should also verify the completed figure against every condition given in the question.
This Practice Set 14 contains 5 fresh NCERT-based MCQs covering construction conditions, diagonals, angles, arcs, and accuracy.
What You Will Learn
✔ Identifying suitable construction data
✔ Understanding the role of diagonals
✔ Locating points using arcs
✔ Constructing specified angles
✔ Checking construction accuracy
✔ Applying geometrical reasoning
Why This Topic Is Important
Practical Geometry develops precision, visualisation, and logical reasoning. It helps students understand how a figure can be uniquely determined from a suitable set of measurements.
These concepts are important for construction-based questions in 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. A quadrilateral $$ABCD$$ is to be constructed using the following information:
$$AB=5\text{ cm}$$
$$BC=6\text{ cm}$$
$$CD=4\text{ cm}$$
$$DA=7\text{ cm}$$
and:
$$BD=8\text{ cm}$$
Which two triangles can be constructed using diagonal $$BD$$?
A) $$\triangle ABD$$ and $$\triangle BCD$$
B) $$\triangle ABC$$ and $$\triangle ACD$$
C) $$\triangle ABD$$ and $$\triangle ACD$$
D) $$\triangle ABC$$ and $$\triangle BCD$$
Answer:
A) $$\triangle ABD$$ and $$\triangle BCD$$
Useful Concept
A diagonal divides a quadrilateral into two triangles.
Solution
The given diagonal is:
$$BD=8\text{ cm}$$
It joins opposite vertices $$B$$ and $$D$$.
Therefore, it divides quadrilateral $$ABCD$$ into:
$$\triangle ABD$$
and:
$$\triangle BCD$$
The diagonal $$BD$$ is common to both triangles.
Hence, the correct answer is:
A) $$\triangle ABD$$ and $$\triangle BCD$$
Q2. A student needs to locate point $$C$$ such that:
$$AC=6\text{ cm}$$
and:
$$BC=8\text{ cm}$$
from two already constructed points $$A$$ and $$B$$. Which statement is correct?
A) Draw arcs with centres $$A$$ and $$B$$
B) Draw an arc only with centre $$C$$
C) Construct an angle without using distances
D) Draw a random line from $$A$$
Answer:
A) Draw arcs with centres $$A$$ and $$B$$
Useful Concept
A point at two known distances from two fixed points can be located using intersecting arcs.
Solution
The required point $$C$$ must satisfy:
$$AC=6\text{ cm}$$
and:
$$BC=8\text{ cm}$$
Therefore:
- Draw an arc with centre $$A$$ and radius $$6\text{ cm}$$.
- Draw another arc with centre $$B$$ and radius $$8\text{ cm}$$.
- Their intersection gives the possible position of $$C$$.
Thus, arcs with centres $$A$$ and $$B$$ are required.
Hence, the correct answer is:
A) Draw arcs with centres $$A$$ and $$B$$
Q3. In a construction, the angle:
$$\angle PQR=75^\circ$$
is given. Which point must be used as the vertex while constructing the angle?
A) $$P$$
B) $$Q$$
C) $$R$$
D) Both $$P$$ and $$R$$
Answer:
**B) $$Q$$
Useful Concept
The middle letter in the name of an angle represents its vertex.
Solution
The given angle is:
$$\angle PQR$$
The middle letter is:
$$Q$$
Therefore, the vertex is:
$$Q$$
The angle:
$$75^\circ$$
must be constructed at point $$Q$$.
Hence, the correct answer is:
**B) $$Q$$
Q4. Which instrument is most suitable for transferring a length from one part of a construction to another without changing its measure?
A) Compass
B) Protractor
C) Eraser
D) Set square only
Answer:
A) Compass
Useful Concept
A compass can be used to transfer a given length accurately.
Solution
Suppose a segment has length:
$$7\text{ cm}$$
The compass can be opened to exactly:
$$7\text{ cm}$$
and then used to mark the same distance elsewhere in the construction.
A protractor is mainly used for measuring or constructing angles.
Therefore, the appropriate instrument for transferring a length is the compass.
Hence, the correct answer is:
A) Compass
Q5. A student is given enough measurements to construct a quadrilateral, but the two arcs used to locate a vertex do not intersect. What is the most appropriate conclusion?
A) The construction or measurements should be checked
B) The vertex can be placed anywhere
C) The arcs should always be ignored
D) The given measurements can be changed immediately
Answer:
A) The construction or measurements should be checked
Useful Concept
If two arcs that should locate a point do not intersect, the construction data or the construction steps need to be examined.
Solution
Suppose point $$C$$ is required to satisfy:
$$AC=a$$
and:
$$BC=b$$
Two arcs are drawn with centres $$A$$ and $$B$$.
If the arcs do not intersect, there is no common point satisfying both distance conditions for the particular construction.
The student should therefore check:
✔ Compass settings
✔ Given measurements
✔ Previously constructed points
✔ Construction steps
The data should not be changed without a valid reason.
Hence, the correct answer is:
A) The construction or measurements should be checked
Important Concepts
Diagonal $$BD$$
In quadrilateral:
$$ABCD$$
diagonal $$BD$$ divides the quadrilateral into:
$$\triangle ABD$$
and:
$$\triangle BCD$$
Locating a Point
If:
$$AC=a$$
and:
$$BC=b$$
then arcs centred at $$A$$ and $$B$$ with radii $$a$$ and $$b$$ can be used to locate $$C$$.
Angle Vertex
For:
$$\angle PQR$$
the vertex is:
$$Q$$
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 and construct angles.
Checking Arcs
If required arcs do not intersect, the construction and measurements should be checked carefully.
Related Practice Questions
Q1. What triangles are formed by diagonal $$BD$$ in quadrilateral $$ABCD$$?
Q2. Which instrument is used to transfer a given length?
Q3. What is the vertex of $$\angle XYZ$$?
Q4. How can point $$C$$ be located if $$AC$$ and $$BC$$ are known?
Q5. What should be checked if two construction arcs do not intersect?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Diagonal $$BD$$ of quadrilateral $$ABCD$$ forms:
A) $$\triangle ABD$$ and $$\triangle BCD$$
B) $$\triangle ABC$$ and $$\triangle ACD$$
C) $$\triangle ABC$$ only
D) No triangles
Q2. Which instrument transfers a length accurately?
A) Compass
B) Protractor
C) Calculator
D) Eraser
Q3. In:
$$\angle XYZ$$
the vertex is:
A) $$X$$
B) $$Y$$
C) $$Z$$
D) None
Q4. If two arcs used to locate a point do not intersect, what should be done?
A) Check the construction and measurements
B) Place the point randomly
C) Ignore the arcs
D) Change every measurement
Q5. A point is required to be:
$$5\text{ cm}$$
from $$A$$ and:
$$7\text{ cm}$$
from $$B$$. Which method is suitable?
A) Two arcs
B) One random line
C) One angle only
D) No construction is possible
Exam Tips
✔ Identify the diagonal before dividing a quadrilateral into triangles.
✔ Use the compass to transfer lengths accurately.
✔ Remember that the middle letter of an angle is its vertex.
✔ Use arcs to locate a point at specified distances from known points.
✔ If arcs do not intersect as expected, check the construction.
✔ Never change given measurements simply to make the construction work.
✔ Verify all conditions after completing the figure.
Quick Revision Notes
✔ $$BD$$ divides $$ABCD$$ into:
$$\triangle ABD$$
and:
$$\triangle BCD$$
✔ Compass → length transfer and arcs.
✔ Protractor → angle construction.
✔ $$\angle PQR$$ → vertex is $$Q$$.
✔ Two distance conditions → two suitable arcs.
✔ Non-intersecting arcs → check measurements and construction.
Common Mistakes Students Make
❌ Using the wrong diagonal.
❌ Constructing an angle at the wrong vertex.
❌ Changing the compass opening while transferring a length.
❌ Using the protractor to transfer a length.
❌ Placing a point randomly when arcs do not intersect.
❌ Not checking the construction data.
Key Takeaways
✔ A diagonal divides a quadrilateral into two triangles.
✔ A compass is useful for transferring lengths.
✔ Arcs can locate points at specified distances.
✔ The middle letter of an angle is its vertex.
✔ A construction must satisfy all given conditions.
✔ Non-intersecting arcs require careful checking of the construction.
FAQs
Q. What triangles are formed by diagonal $$BD$$?
Answer:
In quadrilateral $$ABCD$$, diagonal $$BD$$ forms:
$$\triangle ABD$$
and:
$$\triangle BCD$$
Q. Which instrument is used to transfer a length?
Answer:
A compass is used to transfer a given length accurately.
Q. What is the vertex of $$\angle PQR$$?
Answer:
The vertex is:
$$Q$$
Q. How can a point at two fixed distances be located?
Answer:
Draw two arcs with the two known points as centres and the specified distances as radii. Their intersection gives the required point or possible points.
Q. What should be done if two required arcs do not intersect?
Answer:
The given measurements, compass settings, and previous construction steps should be checked carefully.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on diagonals, point location, angles, compass usage, and construction verification.
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