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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.

Problem Solving Using Properties of Quadrilaterals

This section applies the properties of quadrilaterals discussed earlier to solve various problems. It includes step-by-step methods to find unknown sides, angles, and diagonals using properties like parallel sides, equal sides, angle sums, and diagonal bisecting. The section emphasizes logical reasoning and the use of geometric properties to deduce missing information. Several examples demonstrate how to use the properties of parallelograms, rectangles, rhombus, and squares to solve problems. It also shows how to use the angle sum property and exterior angle property effectively. This section strengthens students' problem-solving skills and prepares them for exams and practical applications.

📊 Diagram: Diagrams show various quadrilaterals with given sides and angles, highlighting the known and unknown quantities. Stepwise annotations demonstrate the application of properties to find missing values.

🧪 Activity: Activity: Solve given problems on quadrilaterals using ruler and protractor for measurement and verification.

🔗 Connection: Leads to the summary section, consolidating all properties and applications learned.

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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