Class 9 Math Chapter 9: All Notes & Resources
Choose a resource below for Chapter 9 Similar Figures, from solved exercises to definitions and MCQs.
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Class 9 Mathematics Chapter 9 explores the concept of similarity in geometry. You will learn to identify similar polygons, understand the relationship between the lengths, areas, and volumes of similar figures, and apply these concepts to solve real-world problems involving scale models and tessellations. This hub gathers every Chapter 9 resource in one place. Start with the Chapter 9 definitions for quick revision, then move to the solved exercises below. For targeted practice, try the Chapter 9 MCQs. You can also review the Grade 9 Math Pairing Scheme to understand paper weightings. When you are done, return to the main Class 9 Mathematics page for the next chapter.
Last updated: October 23, 2026
Exercise 9.1 Solved
Identify similar solids and triangles, prove similarity, and find unknown side lengths using the properties of proportional sides.
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Exercise 9.2 Solved
Calculate the ratio of areas of similar figures and find unknown areas given the ratio of corresponding side lengths.
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Exercise 9.3 Solved
Determine the ratio of volumes for similar solids and solve problems involving the capacity and mass of similar objects.
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Exercise 9.4 Solved
Explore the geometrical properties of regular polygons, triangles, and parallelograms, and learn about real-world applications like tessellation.
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Chapter 9 Definitions
All key definitions and formulas for similar figures, regular polygons, area and volume ratios, and tessellation.
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Chapter 9 MCQs
Multiple-choice questions covering the entire chapter with detailed solutions, perfect for exam preparation and self-testing.
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Muhammad Tayyab
Subject Specialist Math
MSc Mathematics · Govt Christian High School Daska, Sialkot, Punjab
Last updated: October 23, 2026
Key Concepts – Similar Figures
Similar Polygons
\(A \sim B\)
Two polygons are similar if their corresponding angles are equal and corresponding sides are proportional.
Ratio of Areas
\(\frac{A_1}{A_2} = \left(\frac{l_1}{l_2}\right)^2\)
The ratio of the areas of similar figures is the square of the ratio of their corresponding lengths.
Ratio of Volumes
\(\frac{V_1}{V_2} = \left(\frac{l_1}{l_2}\right)^3\)
The ratio of the volumes of similar solids is the cube of the ratio of their corresponding lengths.
Interior Angle of Polygon
\(\frac{(n-2) \times 180^{\circ}}{n}\)
The formula to find the measure of each interior angle of a regular \(n\)-sided polygon.
Exterior Angle of Polygon
\(\frac{360^{\circ}}{n}\)
The formula to find the measure of each exterior angle of a regular \(n\)-sided polygon.
Tessellation
Sum of angles = \(360^{\circ}\)
A pattern of shapes that fit together perfectly without gaps. Only regular triangles, squares, and hexagons can tessellate.
Chapter 9 Frequently Asked Questions
What are similar figures?
Similar figures have the same shape but not necessarily the same size. For polygons to be similar, their corresponding angles must be equal, and their corresponding sides must be proportional.
What is the relationship between the area and volume of similar figures?
If the ratio of corresponding lengths of two similar figures is \(a:b\), then the ratio of their areas is \(a^2:b^2\), and the ratio of their volumes (if they are solids) is \(a^3:b^3\).
What is a regular polygon?
A regular polygon is a polygon that has all sides equal in length and all interior angles equal in measure. Examples include equilateral triangles, squares, and regular hexagons.
What is tessellation?
Tessellation is a pattern of shapes that fit together perfectly to cover a flat surface without any gaps or overlaps. Regular polygons like triangles, squares, and hexagons can tessellate.
How is the mass of a similar solid related to its volume?
For solids made of the same material, mass is directly proportional to volume. Therefore, the ratio of their masses is equal to the ratio of their volumes, which is the cube of the ratio of their corresponding lengths.
Created by Hira Science Academy | Aligned with Punjab Board 2027 Syllabus