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Quadrilaterals

    Introduction

    Interior and Exterior of a Quadrilateral

    Convex and concave polygons

    Angle-sum property of a quadrilateral

    Types of Quadrilaterals

    Exercise 12.1

    Exercise 12.2

    Looking Back

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Quadrilaterals > Easy Level Worksheet

Easy Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

Note: Answer each question carefully. Draw neat diagrams where required and label all vertices.

In this easy level, we'll learn the basics of quadrilaterals, their properties, and different types.

Let's explore the fascinating world of four-sided figures!

1. How many sides does a quadrilateral have?

A quadrilateral has sides

Perfect! 'Quad' means four, so a quadrilateral has 4 sides.

2. What is the sum of the interior angles of a quadrilateral?

Sum of interior angles = °

Excellent! The angle sum property: all angles add up to 360°.

3. Name any two examples of quadrilaterals.

Example 1:

Example 2: or or

Great! Common quadrilaterals include square, rectangle, parallelogram, rhombus, trapezium, and kite.

4. How many diagonals does a quadrilateral have?

Number of diagonals =

Correct! A quadrilateral has exactly 2 diagonals.

5. What is the name of a quadrilateral with both pairs of opposite sides parallel?

Name:

Perfect! When both pairs of opposite sides are parallel, it's a parallelogram.

6. Name the quadrilateral with all sides equal and all angles right angles.

This quadrilateral is a

Excellent! A square has all sides equal AND all angles equal to 90°.

7. What is a diagonal?

A diagonal is a line segment joining

Correct! Diagonals connect vertices that are not next to each other.

8. Write one property of a rectangle.

Property: or

Great! Rectangles have all angles equal to 90° and opposite sides equal.

9. Write one property of a square.

Property: or

Perfect! Squares have all sides equal and all angles equal to 90°.

10. Name the quadrilateral which has only one pair of parallel sides.

Name:

Excellent! A trapezium has exactly one pair of parallel sides.

Drag each property to its correct quadrilateral:

All sides equal, all angles 90°
All angles 90°, opposite sides equal
Both pairs of opposite sides parallel
Only one pair of parallel sides
4 equal sides and 4 right angles
4 right angles
Opposite sides equal and parallel
One pair parallel
Square
Rectangle
Parallelogram
Trapezium

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Find the sum of angles of a quadrilateral.

The sum of all interior angles of a quadrilateral = °

This is the of quadrilaterals

Perfect! This property applies to ALL quadrilaterals.

2. The angles of a quadrilateral are 90°, 85°, 110°, and x°. Find x.

Sum of all angles = °

90 + 85 + 110 + x = 360

+ x = 360

x = 360 - 285 = °

Excellent! The fourth angle is 75°.

3. In a rectangle, each angle is 90°. Find the sum of all angles.

Each angle = °

Number of angles =

Sum = 90 × 4 = °

Great! This verifies the angle sum property.

4. Name all types of quadrilaterals.

Type 1:

Type 2:

Type 3:

Type 4:

Type 5:

Type 6:

Perfect! These are the main types of quadrilaterals.

5. Write any two properties of a parallelogram.

Property 1: Opposite sides are and

Property 2: Opposite angles are

Excellent! These are key properties of parallelograms.

6. Write any two properties of a rhombus.

Property 1: All sides are

Property 2: Diagonals are to each other

Great! Rhombus has equal sides and perpendicular diagonals.

7. In a quadrilateral, three angles are 80°, 90°, and 100°. Find the fourth angle.

Sum of three angles = 80 + 90 + 100 = °

Fourth angle = 360 - 270 = °

Perfect! The fourth angle is 90°.

8. Write any two properties of a trapezium.

Property 1: It has pair of sides

Property 2: The other pair of sides are

Excellent! Trapezium has exactly one pair of parallel sides.

9. Draw a rough sketch of a parallelogram and label its vertices.

Draw on your answer sheet:

Label the four vertices as , , ,

Opposite sides AB and are parallel

Opposite sides AD and are parallel

Great! Make sure opposite sides look parallel in your sketch.

10. Write the difference between a square and a rectangle.

Square: All sides are

Rectangle: Only sides are equal

Both have: All angles = °

Perfect! The main difference is in the side lengths.

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. A rectangle has:

(a) 2 equal sides (b) 4 equal sides (c) 3 equal sides (d) None

2 equal sides
4 equal sides
3 equal sides
None

Correct! A rectangle has opposite sides equal (2 pairs of equal sides).

7. The quadrilateral with only one pair of parallel sides is:

(a) Parallelogram (b) Trapezium (c) Square (d) Kite

Parallelogram
Trapezium
Square
Kite

Perfect! Trapezium has exactly one pair of parallel sides.

8. Opposite sides are equal and parallel in a:

(a) Rectangle (b) Rhombus (c) Both (d) None

Rectangle
Rhombus
Both
None

Excellent! Both rectangle and rhombus are parallelograms with opposite sides equal and parallel.

9. All angles of a rectangle are:

(a) 45° (b) 60° (c) 90° (d) 120°

45°
60°
90°
120°

Correct! All angles in a rectangle are right angles (90°).

10. Diagonals of a square are:

(a) Equal (b) Unequal (c) Perpendicular (d) Both equal and perpendicular

Equal
Unequal
Perpendicular
Both equal and perpendicular

Perfect! Square diagonals are both equal in length AND perpendicular to each other.

🎉 Fantastic Work! You've Mastered Basic Quadrilaterals!

Here's what you learned:

  • What is a Quadrilateral?:

    Definition:

    • A closed figure with 4 sides
    • A closed figure with 4 vertices
    • A closed figure with 4 angles

    Examples:

    • Square, Rectangle, Parallelogram
    • Rhombus, Trapezium, Kite

  • Angle Sum Property:

    • Sum of all interior angles = 360°
    • This applies to ALL quadrilaterals
    • Formula: ∠A + ∠B + ∠C + ∠D = 360°
    • Use this to find missing angles

  • Diagonals:

    • Line segments joining non-adjacent vertices
    • Every quadrilateral has exactly 2 diagonals
    • Different quadrilaterals have different diagonal properties

  • Types of Quadrilaterals:

    Square:

    • All 4 sides equal
    • All 4 angles equal (90° each)
    • Diagonals are equal and perpendicular

    Rectangle:

    • Opposite sides equal
    • All 4 angles equal (90° each)
    • Diagonals are equal

    Parallelogram:

    • Opposite sides equal and parallel
    • Opposite angles equal
    • Diagonals bisect each other

    Rhombus:

    • All 4 sides equal
    • Opposite angles equal
    • Diagonals are perpendicular

    Trapezium:

    • Exactly one pair of parallel sides
    • Other pair is non-parallel

    Kite:

    • Two pairs of adjacent sides equal
    • One diagonal bisects the other

  • Key Properties:

    • Opposite sides: Can be equal, parallel, or both
    • Opposite angles: Can be equal
    • Adjacent angles: Can be supplementary
    • Diagonals: Can be equal, perpendicular, or bisect each other

  • Finding Missing Angles:

    • Use angle sum property: Sum = 360°
    • Add known angles
    • Subtract from 360° to find missing angle
    • Example: If three angles are 80°, 90°, 100°
      • Sum = 80 + 90 + 100 = 270°
      • Fourth angle = 360 - 270 = 90°

  • Common Mistakes to Avoid:

    • Don't confuse square with rectangle (square has all sides equal)
    • Don't confuse parallelogram with trapezium (trapezium has only one pair parallel)
    • Remember: Sum is always 360°, not 180°
    • Don't forget to label vertices in diagrams

Understanding quadrilaterals builds the foundation for geometry and real-world applications!