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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, sides, angles, diagonals, and construction criteria.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 10
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
A quadrilateral can be constructed uniquely when enough suitable measurements are provided. In practical geometry, students learn different sets of information that can determine a quadrilateral, such as four sides and one diagonal, three sides and two diagonals, two adjacent sides and three angles, or three sides and two included angles.
Understanding these conditions helps students decide which construction method should be used.
This Practice Set 10 contains 5 fresh MCQs based on NCERT concepts related to the conditions required for constructing a unique quadrilateral.
What You Will Learn
✔ Understanding conditions for unique construction
✔ Identifying sufficient geometrical information
✔ Using diagonals in construction
✔ Understanding adjacent sides and angles
✔ Selecting the correct construction method
✔ Applying construction concepts to MCQs
Why This Topic Is Important
The main objective of Practical Geometry is not only to draw figures but also to understand which measurements are sufficient to determine a figure uniquely.
These concepts are especially important for examination questions where students must identify whether the given information is sufficient for construction.
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 information is sufficient for constructing a unique quadrilateral?
A) Four sides and one diagonal
B) One side only
C) One angle only
D) Two sides only
Answer:
A) Four sides and one diagonal
Useful Concept
A quadrilateral can be constructed uniquely when four sides and one diagonal are given.
Solution
Consider quadrilateral:
$$ABCD$$
Suppose the four sides:
$$AB,\ BC,\ CD,\ DA$$
and one diagonal:
$$AC$$
are known.
The diagonal $$AC$$ divides the quadrilateral into two triangles:
$$\triangle ABC$$
and:
$$\triangle ACD$$
The triangles can then be constructed using the given side lengths and the diagonal.
Therefore, the given information is sufficient for constructing the quadrilateral uniquely.
Hence, the correct answer is:
A) Four sides and one diagonal
Q2. Which of the following information is sufficient for constructing a unique quadrilateral according to the construction criteria studied in NCERT?
A) Three sides and two diagonals
B) Two sides only
C) One diagonal only
D) Two angles only
Answer:
A) Three sides and two diagonals
Useful Concept
Three sides and two diagonals provide sufficient information to determine a quadrilateral uniquely.
Solution
Consider quadrilateral:
$$ABCD$$
Suppose three sides and two diagonals are known:
$$AB,\ BC,\ CD$$
and:
$$AC,\ BD$$
The two diagonals provide important distance information about the opposite vertices.
Together with the three known sides, these measurements are sufficient to determine the required quadrilateral through construction.
Therefore, the correct answer is:
A) Three sides and two diagonals
Q3. A quadrilateral has two adjacent sides of lengths:
$$AB=6\text{ cm}$$
and:
$$BC=5\text{ cm}$$
along with three angles:
$$\angle A=70^\circ$$
$$\angle B=100^\circ$$
and:
$$\angle C=80^\circ$$
Is this type of information sufficient for constructing the quadrilateral uniquely?
A) Yes
B) No, because only one side is known
C) No, because angles cannot be used
D) No, because quadrilaterals cannot be constructed using angles
Answer:
A) Yes
Useful Concept
A quadrilateral can be constructed uniquely when two adjacent sides and three angles are given.
Solution
The two adjacent sides are:
$$AB=6\text{ cm}$$
and:
$$BC=5\text{ cm}$$
The three angles are:
$$\angle A=70^\circ$$
$$\angle B=100^\circ$$
and:
$$\angle C=80^\circ$$
This provides sufficient information to determine the shape and position of the quadrilateral.
The construction can begin with one of the known sides, followed by constructing the required angles and locating the remaining vertices.
Therefore, this information is sufficient.
Hence, the correct answer is:
A) Yes
Q4. Which of the following combinations represents another valid set of information for constructing a unique quadrilateral?
A) Three sides and two included angles
B) One side and one angle
C) Two angles only
D) One diagonal and one side
Answer:
A) Three sides and two included angles
Useful Concept
Three sides and two included angles provide sufficient information for constructing a unique quadrilateral.
Solution
Suppose a quadrilateral has three known sides and two angles, where the given angles are appropriately located between the known sides.
This information allows the construction to proceed by:
- Drawing a known side.
- Constructing the required included angle.
- Marking the next known side.
- Constructing the second required angle.
- Using the remaining side information to complete the figure.
Thus, three sides and two included angles form a sufficient set of construction information.
Hence, the correct answer is:
A) Three sides and two included angles
Q5. A student is given only the four angles of a quadrilateral. Can the quadrilateral generally be constructed uniquely from these angles alone?
A) Yes, always
B) No, additional length information is required
C) Yes, because four angles determine all side lengths
D) No quadrilateral can have four angles
Answer:
B) No, additional length information is required
Useful Concept
Angles determine the angular relationships of a figure, but they do not generally determine its exact size.
Solution
Suppose the four angles of a quadrilateral are known.
Even if all four angles are fixed, the quadrilateral can generally be enlarged or reduced while preserving those angle measures.
For example, different quadrilaterals can have the same angle measures but different side lengths.
Therefore, additional information such as a side length or other suitable measurement is required to determine the quadrilateral uniquely.
Hence, the correct answer is:
B) No, additional length information is required
Important Concepts
Four Sides and One Diagonal
A quadrilateral can be uniquely constructed when:
Four sides + one diagonal
are given.
Three Sides and Two Diagonals
Another sufficient set is:
Three sides + two diagonals
Two Adjacent Sides and Three Angles
A quadrilateral can also be constructed when:
Two adjacent sides + three angles
are given.
Three Sides and Two Included Angles
Another useful construction condition is:
Three sides + two included angles
Angles Alone
Knowing only the four angles does not generally determine the size of a quadrilateral.
Additional length information is required.
Related Practice Questions
Q1. Can four sides and one diagonal determine a quadrilateral uniquely?
Q2. What happens when a diagonal divides a quadrilateral into two triangles?
Q3. Is one side and one angle enough to construct a unique quadrilateral?
Q4. Why are length measurements important along with angles?
Q5. Name any two sets of information sufficient for constructing a unique quadrilateral.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which set is sufficient for constructing a unique quadrilateral?
A) Four sides and one diagonal
B) One side only
C) One angle only
D) Two angles only
Q2. Which set is also sufficient?
A) Three sides and two diagonals
B) One diagonal only
C) Two sides only
D) One side and one angle
Q3. Which combination can be used for unique construction?
A) Two adjacent sides and three angles
B) One side and two angles
C) Two angles only
D) One diagonal only
Q4. Can four angles alone generally determine the size of a quadrilateral?
A) Yes
B) No
C) Only for every rectangle
D) Only for every square
Q5. Which information includes both length and angular data?
A) Three sides and two included angles
B) Four angles only
C) One angle only
D) Two angles only
Exam Tips
✔ Memorise the important construction criteria.
✔ Remember that four sides and one diagonal are sufficient.
✔ Three sides and two diagonals can also determine a unique quadrilateral.
✔ Two adjacent sides and three angles provide sufficient information.
✔ Three sides and two included angles can also be used.
✔ Angles alone generally do not determine the exact size of a quadrilateral.
✔ Always identify whether the given measurements are sufficient before starting construction.
Quick Revision Notes
✔ Four sides + one diagonal → sufficient for unique construction.
✔ Three sides + two diagonals → sufficient.
✔ Two adjacent sides + three angles → sufficient.
✔ Three sides + two included angles → sufficient.
✔ Four angles alone → generally not sufficient.
✔ Length measurements help determine the size of the quadrilateral.
✔ Diagonals can divide a quadrilateral into two triangles.
Common Mistakes Students Make
❌ Assuming that four angles alone determine a unique quadrilateral.
❌ Forgetting the importance of a diagonal.
❌ Confusing adjacent sides with opposite sides.
❌ Ignoring whether an angle is an included angle.
❌ Starting construction without checking whether sufficient information is available.
❌ Assuming that any combination of measurements will produce a unique quadrilateral.
Key Takeaways
✔ A unique quadrilateral requires sufficient independent information.
✔ Four sides and one diagonal are sufficient.
✔ Three sides and two diagonals are sufficient.
✔ Two adjacent sides and three angles are sufficient.
✔ Three sides and two included angles are sufficient.
✔ Four angles alone generally cannot determine the exact size of a quadrilateral.
✔ Understanding construction criteria makes Practical Geometry easier to solve.
FAQs
Q. What information is sufficient to construct a unique quadrilateral?
Answer:
Some important sets are:
Four sides and one diagonal
Three sides and two diagonals
Two adjacent sides and three angles
Three sides and two included angles
Q. Why is a diagonal useful in quadrilateral construction?
Answer:
A diagonal divides a quadrilateral into two triangles and provides additional information needed to locate the vertices.
Q. Are four angles enough to construct a unique quadrilateral?
Answer:
Generally, no. Additional length information is required to determine its exact size.
Q. What are adjacent sides?
Answer:
Adjacent sides are two sides that share a common vertex.
For example, in quadrilateral:
$$ABCD$$
the sides $$AB$$ and $$BC$$ are adjacent.
Q. What is an included angle?
Answer:
An included angle is the angle formed between two specified sides that meet at a common vertex.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on the important conditions required for constructing a unique quadrilateral.
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