Class 8 Maths Understanding Quadrilaterals Notes

Understanding Quadrilaterals – Quick Notes

Definition:

A quadrilateral is a polygon with four sides and four angles.

• The sum of the interior angles of a quadrilateral is always:

$$(4-2) \times 180^\circ = 360^\circ$$(4−2)×180∘=360∘

Types of Quadrilaterals:

Properties / Formulas:

1. Sum of angles: $\angle A + \angle B + \angle C + \angle D = 360^\circ$∠A+∠B+∠C+∠D=360∘
2. Diagonals of parallelogram bisect each other.
3. Diagonals of rectangle are equal.
4. Diagonals of rhombus are perpendicular.
5. Area formulas:
   • Rectangle: $l \times b$l×b
   • Square: $\text{side}^2$side2
   • Parallelogram: $b \times h$b×h
   • Trapezium: $\frac{1}{2}(sum\ of\ parallel\ sides) \times h$21​(sum of parallel sides)×h
   • Rhombus: $\frac{1}{2} \times (d_1 \times d_2)$21​×(d1​×d2​)

Tips / Tricks:

• Always draw a figure to understand relationships.
• Check diagonals for perpendicularity and equality for identification.
• Use angle sum property $360^\circ$360∘ for missing angles.

Understanding Quadrilaterals – MCQ Q&A

1. Q: How many sides does a quadrilateral have?
   A: 4
2. Q: Sum of interior angles of a quadrilateral?
   A: 360°
3. Q: Opposite sides equal and parallel, opposite angles equal. Which quadrilateral?
   A: Parallelogram
4. Q: All sides equal, all angles 90°?
   A: Square
5. Q: Opposite sides equal, angles 90°, diagonals equal?
   A: Rectangle
6. Q: Diagonals perpendicular, all sides equal?
   A: Rhombus
7. Q: Only one pair of opposite sides parallel?
   A: Trapezium
8. Q: Two pairs of adjacent sides equal, diagonals perpendicular?
   A: Kite
9. Q: Diagonals bisect each other. Which quadrilateral?
   A: Parallelogram, rectangle, square, rhombus
10. Q: Diagonals equal and perpendicular. Which quadrilateral?
    A: Square
11. Q: Area of a parallelogram formula?
    A: Base × Height
12. Q: Area of a trapezium formula?
    A: $\frac{1}{2} (sum\ of\ parallel\ sides) × height$21​(sum of parallel sides)×height
13. Q: A quadrilateral with no sides equal and no sides parallel?
    A: General quadrilateral
14. Q: Which quadrilateral has diagonals that bisect at right angles?
    A: Rhombus and square
15. Q: Can a rectangle be a square?
    A: Yes, if all sides are equal
16. Q: Can a rhombus be a square?
    A: Yes, if all angles are 90°
17. Q: Sum of two adjacent angles of a parallelogram?
    A: 180°
18. Q: Sum of angles of a kite?
    A: 360°
19. Q: Diagonals of a rectangle are perpendicular?
    A: No
20. Q: Area of a square with side 5 cm?
    A: $5^2 = 25\ cm^2$52=25 cm2