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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn convex polygons, regular polygons, angle properties, diagonals, parallelogram, rectangle, square, and trapezium with detailed solutions for CBSE exams.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Understanding Quadrilaterals
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Understanding Quadrilaterals is an important geometry chapter that explains the properties of polygons and different types of quadrilaterals. Mastering these concepts helps students solve geometry questions accurately and prepares them for higher-level mathematics.
What You Will Learn?
✔ Convex and Concave Polygons
✔ Regular Polygons
✔ Interior Angle Sum Property
✔ Exterior Angle Property
✔ Diagonals
✔ Parallelogram
✔ Rectangle
✔ Square and Trapezium
Why This Topic Is Important?
Quadrilaterals and polygons are used in construction, engineering, architecture, and graphic design. Understanding their properties improves logical reasoning and geometric problem-solving skills.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which of the following is a convex quadrilateral?
A) A quadrilateral with one interior angle greater than $$180^\circ$$
B) A quadrilateral in which all interior angles are less than $$180^\circ$$
C) A self-intersecting quadrilateral
D) None of these
Answer:
A quadrilateral in which all interior angles are less than $$180^\circ$$
Useful Formula for this Question:
In a convex polygon:
- Every interior angle is less than $$180^\circ$$.
Concept Behind This Question:
Students should distinguish between convex and concave polygons.
Step-by-Step Solution:
A convex quadrilateral has all its interior angles less than $$180^\circ$$ and all diagonals lie inside the figure.
Therefore, the correct answer is:
A quadrilateral in which all interior angles are less than $$180^\circ$$
Exam Tip:
If any interior angle exceeds $$180^\circ$$, the polygon is concave.
Q2. How many sides does a decagon have?
A) $$8$$
B) $$9$$
C) $$10$$
D) $$12$$
Answer:
$$10$$
Useful Formula for this Question:
A decagon is a polygon having:
$$10$$ sides.
Concept Behind This Question:
Students should remember the names of common polygons.
Step-by-Step Solution:
A decagon consists of:
- $$10$$ sides
- $$10$$ vertices
- $$10$$ angles
Therefore, the correct answer is:
$$10$$
Exam Tip:
Remember:
Pentagon = $$5$$, Hexagon = $$6$$, Octagon = $$8$$, Decagon = $$10$$.
Q3. Which quadrilateral always has four right angles?
A) Rhombus
B) Rectangle
C) Kite
D) Trapezium
Answer:
$$\text{Rectangle}$$
Useful Formula for this Question:
Each interior angle of a rectangle is:
$$90^\circ$$
Concept Behind This Question:
Students should identify the properties of a rectangle.
Step-by-Step Solution:
A rectangle has:
- Four right angles.
- Opposite sides equal and parallel.
Therefore, the correct answer is:
$$\text{Rectangle}$$
Exam Tip:
A square is also a rectangle because it has four right angles.
Q4. A regular polygon has each exterior angle equal to $$45^\circ$$. How many sides does it have?
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
$$8$$
Useful Formula for this Question:
$$\text{Exterior Angle}=\frac{360^\circ}{n}$$
Concept Behind This Question:
Students should determine the number of sides using the exterior angle formula.
Step-by-Step Solution:
Given:
$$\frac{360^\circ}{n}=45^\circ$$
Therefore,
$$n=\frac{360}{45}=8$$
Hence, the polygon has:
$$8$$ sides.
Therefore, the correct answer is:
$$8$$
Exam Tip:
Divide $$360^\circ$$ by the exterior angle to find the number of sides.
Q5. Which statement is true for a square?
A) Opposite sides are unequal.
B) Diagonals are unequal.
C) All sides are equal and all angles are $$90^\circ$$.
D) Only one pair of sides is parallel.
Answer:
All sides are equal and all angles are $$90^\circ$$.
Useful Formula for this Question:
Properties of a square:
- Four equal sides.
- Four right angles.
- Opposite sides are parallel.
Concept Behind This Question:
Students should know the complete properties of a square.
Step-by-Step Solution:
A square satisfies all of the following:
- All sides are equal.
- Each angle is $$90^\circ$$.
- Opposite sides are parallel.
- Diagonals are equal.
Therefore, the correct answer is:
All sides are equal and all angles are $$90^\circ$$.
Exam Tip:
A square is both a rectangle and a rhombus.
Important Formulas & Concepts
1. Sum of Interior Angles of a Polygon
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles of Any Polygon
$$360^\circ$$
3. Number of Diagonals
$$\frac{n(n-3)}{2}$$
4. Exterior Angle of a Regular Polygon
$$\frac{360^\circ}{n}$$
5. Properties of a Rectangle
- Opposite sides are equal.
- Opposite sides are parallel.
- All angles are $$90^\circ$$.
6. Properties of a Square
- Four equal sides.
- Four right angles.
- Diagonals are equal and bisect each other.
FAQs
1. What is a convex polygon?
A convex polygon has all interior angles less than $$180^\circ$$.
2. How many sides does a decagon have?
$$10$$
3. What is the exterior angle sum of a polygon?
$$360^\circ$$
4. Is every square a rectangle?
Yes, every square is a rectangle.
5. How do you find the number of sides of a regular polygon?
Use:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Common Mistakes
❌ Confusing convex and concave polygons.
❌ Forgetting the exterior angle formula.
❌ Mixing the properties of a square and a rectangle.
❌ Using the wrong polygon names.
❌ Incorrect calculation of the number of sides.
Quick Revision Notes
✔ Convex polygons have all interior angles less than $$180^\circ$$.
✔ Decagon has $$10$$ sides.
✔ Rectangle has four right angles.
✔ Square has equal sides and equal angles.
✔ Exterior angles of any polygon add up to $$360^\circ$$.
✔ Number of sides of a regular polygon:
$$n=\frac{360^\circ}{\text{Exterior Angle}}$$
Conclusion
Understanding Quadrilaterals is a key chapter in Class 8 Mathematics. Learning the properties of polygons and quadrilaterals helps students solve geometry problems efficiently and prepares them for advanced mathematical concepts. Regular MCQ practice improves speed, accuracy, and conceptual understanding.
Related links
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