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Practice Class 8 Maths Chapter 3 Understanding Quadrilaterals MCQ Questions with Answers based on NCERT syllabus. Learn regular polygons, diagonals, angle sum property, kite, parallelogram, and quadrilateral properties 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 introduces students to different types of polygons and quadrilaterals along with their properties. It helps develop logical reasoning and geometric visualization, which are essential for solving geometry-based questions.
What You Will Learn?
✔ Regular and Irregular Polygons
✔ Quadrilaterals
✔ Interior and Exterior Angles
✔ Diagonals
✔ Kite
✔ Parallelogram
✔ Rectangle and Square
✔ Geometry Problem Solving
Why This Topic Is Important?
The concepts of quadrilaterals are widely used in mathematics, engineering, architecture, map design, and construction. Understanding these concepts helps students solve geometry problems with confidence.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. A regular polygon is a polygon in which:
A) Only sides are equal
B) Only angles are equal
C) Both sides and angles are equal
D) No sides are equal
Answer:
$$\text{Both sides and angles are equal}$$
Useful Formula for this Question:
A regular polygon has:
- Equal sides
- Equal interior angles
Concept Behind This Question:
Students should understand the definition of a regular polygon.
Step-by-Step Solution:
In a regular polygon:
- All sides are equal.
- All interior angles are equal.
Therefore, the correct answer is:
$$\text{Both sides and angles are equal}$$
Exam Tip:
Equal sides alone do not make a polygon regular; equal angles are also required.
Q2. How many diagonals does a pentagon have?
A) $$3$$
B) $$4$$
C) $$5$$
D) $$6$$
Answer:
$$5$$
Useful Formula for this Question:
Number of diagonals:
$$\frac{n(n-3)}{2}$$
Concept Behind This Question:
Students should calculate the number of diagonals using the formula.
Step-by-Step Solution:
For a pentagon,
$$n=5$$
$$\frac{5(5-3)}{2}$$
$$=\frac{5\times2}{2}$$
$$=5$$
Therefore, the correct answer is:
$$5$$
Exam Tip:
Remember the diagonal formula for polygons.
Q3. Which quadrilateral has two pairs of adjacent equal sides?
A) Rectangle
B) Kite
C) Square
D) Trapezium
Answer:
$$\text{Kite}$$
Useful Formula for this Question:
A kite has:
- Two pairs of adjacent equal sides.
Concept Behind This Question:
Students should identify the properties of a kite.
Step-by-Step Solution:
A kite is a quadrilateral in which:
- Two pairs of adjacent sides are equal.
- One pair of opposite angles is equal.
Therefore, the correct answer is:
$$\text{Kite}$$
Exam Tip:
Adjacent equal sides indicate a kite.
Q4. Find the sum of the interior angles of a pentagon.
A) $$360^\circ$$
B) $$540^\circ$$
C) $$720^\circ$$
D) $$900^\circ$$
Answer:
$$540^\circ$$
Useful Formula for this Question:
$$ (n-2)\times180^\circ $$
Concept Behind This Question:
Students should apply the interior angle sum formula.
Step-by-Step Solution:
For a pentagon,
$$n=5$$
$$ (5-2)\times180^\circ $$
$$=3\times180^\circ$$
$$=540^\circ$$
Therefore, the correct answer is:
$$540^\circ$$
Exam Tip:
Subtract $$2$$ from the number of sides before multiplying by $$180^\circ$$.
Q5. Which of the following is always a parallelogram?
A) Kite
B) Trapezium
C) Rectangle
D) Pentagon
Answer:
$$\text{Rectangle}$$
Useful Formula for this Question:
Every rectangle has:
- Opposite sides equal and parallel.
Concept Behind This Question:
Students should understand the relationship between different quadrilaterals.
Step-by-Step Solution:
A rectangle satisfies all the properties of a parallelogram because:
- Opposite sides are equal.
- Opposite sides are parallel.
- Opposite angles are equal.
Therefore, every rectangle is a parallelogram.
Hence, the correct answer is:
$$\text{Rectangle}$$
Exam Tip:
Remember:
Square ⟶ Rectangle ⟶ Parallelogram.
Important Formulas & Concepts
1. Sum of Interior Angles of a Polygon
$$ (n-2)\times180^\circ $$
2. Sum of Exterior Angles
$$360^\circ$$
3. Number of Diagonals
$$\frac{n(n-3)}{2}$$
4. Regular Polygon
All sides and all interior angles are equal.
5. Kite
A quadrilateral having two pairs of adjacent equal sides.
6. Rectangle
- Opposite sides are equal.
- Opposite sides are parallel.
- Each angle is $$90^\circ$$.
FAQs
1. What is a regular polygon?
A polygon having all sides and all angles equal.
2. How many diagonals does a pentagon have?
$$5$$
3. What is a kite?
A quadrilateral with two pairs of adjacent equal sides.
4. Is every rectangle a parallelogram?
Yes.
5. What is the interior angle sum of a pentagon?
$$540^\circ$$
Common Mistakes
❌ Confusing a kite with a rhombus.
❌ Using the wrong value of $$n$$ in formulas.
❌ Forgetting the diagonal formula.
❌ Assuming every quadrilateral is a parallelogram.
❌ Mixing regular and irregular polygons.
Quick Revision Notes
✔ Regular polygons have equal sides and equal angles.
✔ Pentagon has $$5$$ diagonals.
✔ A kite has adjacent equal sides.
✔ Every rectangle is a parallelogram.
✔ Exterior angle sum is always $$360^\circ$$.
✔ Interior angle sum formula:
$$ (n-2)\times180^\circ $$
Conclusion
Understanding Quadrilaterals is an important chapter in Class 8 Mathematics. Learning the properties of polygons, diagonals, and special quadrilaterals strengthens geometric concepts and improves problem-solving skills. Regular MCQ practice helps students achieve better accuracy and confidence in examinations.
Related links
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-2
- Class 8 Maths Chapter 3 Understanding Quadrilaterals part-1
- Class 8 Maths Chapter 2 Linear Equations in One Variable part-11
- Class 8 Maths Chapter 2 Linear Equations in One Variable – part 10
- Class 8 Maths Chapter 2 Linear Equations in One Variable – Part 9
- Class 8 Maths Chapter 2 Linear Equations in One Variable- Part 8
- Class 8 Maths Chapter 2 Linear Equations in One Variable- Part 7
- Class 8 Maths Chapter 2 Linear Equations in One Variable- Part 6
- Class 8 Maths Chapter 2 Linear Equations in One Variable transposition method- Part 5
- Class 8 Maths Chapter 2 Linear Equations in One Variable – Part 4
- Class8 Maths Chapter2 Transposition method, variables – Part 3
- Class 8 Maths Chapter 1 Rational Numbers- Part 10
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