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MathematicsClass 8Quadrilaterals

Quadrilaterals | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 3 min read

Quadrilaterals – this guide gives you a concise, exam-ready overview of Quadrilaterals from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Types of Quadrilaterals

This section classifies quadrilaterals into various types based on their sides and angles. The main types discussed are trapezium, parallelogram, rectangle, square, and rhombus. Each type has specific properties that distinguish it from others. A trapezium has only one pair of parallel sides. A parallelogram has two pairs of parallel sides, and opposite sides are equal in length. A rectangle is a parallelogram with all angles equal to 90 degrees. A square is a rectangle with all sides equal, making it both equilateral and equiangular. A rhombus is a parallelogram with all sides equal but angles are not necessarily 90 degrees. The section explains these properties in detail, supported by diagrams. Understanding these types helps in solving problems related to perimeter, area, and angle calculations.

📊 Diagram: Diagrams show each type of quadrilateral labeled with sides and angles: trapezium with one pair of parallel sides, parallelogram with opposite sides parallel and equal, rectangle with right angles, square with equal sides and right angles, and rhombus with equal sides but non-right angles.

🧪 Activity: Activity: Students classify given quadrilaterals by measuring sides and angles using rulers and protractors to identify their types.

🔗 Connection: This section prepares students to study the properties of parallelograms in the next section.

Frequently asked questions

1. Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm.

Solution: Each equilateral triangle has all sides equal to 4 cm and all angles equal to 60°. When two equilateral triangles are joined along one side, the quadrilateral formed has:

  • Two sides of length 4 cm (the joined side is common and internal).
  • The other sides are also 4 cm each (the remaining sides of the triangles).
  • The angles at the joined side will be 120° each (since the two 60° angles add up).
  • The other angles remain 60° each.

Thus, the quadrilateral has sides 4 cm, 4 cm, 4 cm,

2. Construct a kite whose diagonals are of lengths 6 cm and 8 cm.

Solution: To construct a kite with diagonals 6 cm and 8 cm: 1. Draw one diagonal of length 8 cm. 2. Find the midpoint of this diagonal. 3. At the midpoint, draw a perpendicular line. 4. On this perpendicular, mark points 3 cm above and below the midpoint (since the other diagonal is 6 cm). 5. Join the endpoints of the 8 cm diagonal to these points to form the kite. 6. Verify that the two pairs of adjacent sides are equal. This construction ensures the kite has diagonals 6 cm and 8 cm intersectin

3. Find the remaining angles in the following trapeziums — 100°, 135°, 105°

Solution: In a trapezium, the sum of the interior angles is 360°. Given angles: 100°, 135°, 105° Sum of given angles = 100 + 135 + 105 = 340° Remaining angle = 360° - 340° = 20° Thus, the missing angle is 20°.

4. Draw a Venn diagram showing the set of parallelograms, kites, rhombuses, rectangles, and squares. Then, answer the following questions — (i) What is the quadrilateral that is both a kite and a parallelogram? (ii) Can there be a quadrilateral that is both a kite and a rectangle? (iii) Is every kite a rhombus? If not, what is the correct relationship between these two types of quadrilaterals?

Solution:

  • Draw a Venn diagram with overlapping sets for parallelograms, kites, rhombuses, rectangles, and squares.

(i) A quadrilateral that is both a kite and a parallelogram is a rhombus because a rhombus has two pairs of adjacent equal sides (kite property) and opposite sides parallel (parallelogram property). (ii) There cannot be a quadrilateral that is both a kite and a rectangle because a kite has two pairs of adjacent equal sides but a rectangle has equal opposite sides and all angles 90

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