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Quadrilaterals – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 4. Notes, key terms, important questions with answers and MCQs.

Chapter overview

A quadrilateral is a closed figure with four sides; its angles add up to 360°. Special quadrilaterals have special sides, angles and diagonals.

Types

Parallelogram: opposite sides parallel and equal; opposite angles equal; diagonals bisect each other.
Rectangle: parallelogram with right angles; equal diagonals.
Rhombus: all sides equal; diagonals perpendicular bisectors.
Square: all sides equal and all angles 90°.
Trapezium: one pair of parallel sides; kite: two pairs of adjacent equal sides.

Angles

Interior angles of any quadrilateral sum to 360°.
Adjacent angles of a parallelogram add to 180°.
Exterior angles of any polygon add to 360°.

Key terms

Diagonal: segment joining two opposite vertices
Kite: quadrilateral with two pairs of equal adjacent sides
Trapezium: a quadrilateral with exactly one pair of parallel sides

Formulas

Angle sum of a polygon with n sides = (n − 2) × 180°
Each exterior angle of a regular n-gon = 360°/n

Important questions with answers

Find the sum of the interior angles of a pentagon.2 marks

(n − 2) × 180° = 3 × 180° = 540°.

Write three properties of a rectangle that a general parallelogram does not have.3 marks

All angles are 90°; the diagonals are equal in length; (it has 2 lines of symmetry, while a general parallelogram has none).

Compare the parallelogram, rectangle, rhombus, square and kite in terms of sides, angles and diagonals.5 marks

Parallelogram: opposite sides equal and parallel, opposite angles equal, diagonals bisect each other. Rectangle: as parallelogram, plus all angles 90° and equal diagonals. Rhombus: as parallelogram, plus all sides equal and diagonals perpendicular. Square: all sides equal, all angles 90°, diagonals equal and perpendicular bisectors of each other. Kite: two pairs of equal adjacent sides, one pair of opposite angles equal, diagonals perpendicular with one bisecting the other.

Quick revision

Quadrilateral angle sum 360°.
Rhombus diagonals cross at 90°.
Rectangle diagonals are equal.

Exam tips

Draw the diagonals to see which quadrilateral you have.
A square is a special rectangle and a special rhombus.

Practice MCQs

Number of sides of a quadrilateral is
1. 3
2. 4
3. 5
4. 6
Show answer
Answer: (b) 4. Four.
Each angle of a rectangle is
1. 90°
2. 60°
3. 120°
4. 45°
Show answer
Answer: (a) 90°. Right angles.
Two angles of a parallelogram are adjacent and one is 65°. The other is
1. 65°
2. 25°
3. 115°
4. 135°
Show answer
Answer: (c) 115°. 180 − 65.
Sum of interior angles of a pentagon is
1. 360°
2. 720°
3. 540°
4. 450°
Show answer
Answer: (c) 540°. (5 − 2) × 180.
Each interior angle of a regular hexagon is
1. 108°
2. 120°
3. 135°
4. 144°
Show answer
Answer: (b) 120°. (6 − 2) × 180/6.
Each exterior angle of a regular polygon is 40°. The number of sides is
1. 8
2. 9
3. 10
4. 12
Show answer
Answer: (b) 9. 360/40.
Which statement is always true?
1. every rhombus is a square
2. every square is a rhombus
3. every rectangle is a square
4. every trapezium is a parallelogram
Show answer
Answer: (b) every square is a rhombus. A square has all sides equal.
In a parallelogram, one angle is 70°. The adjacent angle is
1. 110°
2. 70°
3. 20°
4. 140°
Show answer
Answer: (a) 110°. Adjacent angles add to 180°.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.