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MathematicsClass 8Understanding Quadrilaterals

Understanding Quadrilaterals | Class 8 Mathematics Notes

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

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

Properties of a Parallelogram

This section delves into the detailed properties of parallelograms. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. The section explains that in a parallelogram, opposite sides are equal in length, and opposite angles are equal. The diagonals of a parallelogram bisect each other, meaning each diagonal divides the other into two equal parts. These properties are proven using geometric reasoning and are fundamental in solving problems involving parallelograms. The section also discusses the concept of adjacent angles being supplementary (sum to 180°). These properties help in identifying parallelograms and distinguishing them from other quadrilaterals. The section includes step-by-step proofs and examples to illustrate these properties clearly.

📊 Diagram: The diagram shows parallelogram ABCD with sides AB parallel to CD and BC parallel to AD. Angles are marked to show equality of opposite angles and supplementary adjacent angles. Diagonals AC and BD intersect at point O, showing the bisecting property.

🧪 Activity: Activity: Using paper folding to verify that diagonals of a parallelogram bisect each other.

🔗 Connection: Leads to the next section on special parallelograms like rectangles, rhombus, and squares, which have additional properties.

Frequently asked questions

Given here are some figures. Classify each of them on the basis of the following. (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon

To classify each figure:

(a) Simple curve: A curve which does not intersect itself. (b) Simple closed curve: A simple curve which ends at the starting point forming a closed shape. (c) Polygon: A simple closed curve made up of line segments. (d) Convex polygon: A polygon where all interior angles are less than 180° and no vertices point inward. (e) Concave polygon: A polygon with at least one interior angle greater than 180°, having an indentation.

Each figure should be examined to see which o

What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides

A regular polygon is a polygon that is both equilateral (all sides equal) and equiangular (all interior angles equal).

(i) A regular polygon with 3 sides is called an equilateral triangle. (ii) A regular polygon with 4 sides is called a square. (iii) A regular polygon with 6 sides is called a regular hexagon.

TRY THESE Take a regular hexagon Fig 3.4. 1. What is the sum of the measures of its exterior angles x, y, z, p, q, r? 2. Is x = y = z = p = q = r? Why? 3. What is the measure of each? (i) exterior angle (ii) interior angle 4. Repeat this activity for the cases of (i) a regular octagon (ii) a regular 20-gon

1. The sum of the measures of the exterior angles x, y, z, p, q, r of any polygon is always 360°.

2. Yes, x = y = z = p = q = r because the hexagon is regular, meaning all sides and angles are equal, so all exterior angles are equal.

3. (i) Each exterior angle = 360° ÷ 6 = 60° (ii) Each interior angle = 180° - 60° = 120°

4. For a regular octagon:

  • Number of sides = 8
  • Each exterior angle = 360° ÷ 8 = 45°
  • Each interior angle = 180° - 45° = 135°

For a regular 20-gon:

  • Number of sides = 20
Example 1: Find measure x in Fig 3.3.

Given the exterior angles in Fig 3.3 are x, 90°, 50°, and 110°.

Sum of exterior angles of any polygon = 360°.

Therefore, x + 90° + 50° + 110° = 360° => x + 250° = 360° => x = 360° - 250° = 110°

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