NCERT Class 8 Maths Chapter 11
Exploring Some Geometric Themes
NCERT Class 8 Maths Chapter 11 (Ganita Prakash Part 2) delves deeper into geometry, exploring the properties of shapes, symmetry, geometric constructions, and transformations. This CBSE chapter builds spatial reasoning skills and helps students see mathematics in architecture, art, and nature. Topics include lines, angles, special triangles, and the properties of circles.
Read Online
Key Terms
- Symmetry
- A property of a figure where one half is a mirror image of the other; a figure has line symmetry if a line divides it into two congruent halves.
- Congruence
- Two figures are congruent if they have exactly the same shape and size — one can be superimposed on the other.
- Similarity
- Two figures are similar if they have the same shape but not necessarily the same size; corresponding angles are equal and sides are in proportion.
- Transformation
- A mapping that moves or changes a geometric figure; types include translation (sliding), reflection (flipping), rotation (turning), and dilation (scaling).
- Tessellation
- A pattern of shapes that tiles a plane without gaps or overlaps; e.g., squares, equilateral triangles, and regular hexagons can tessellate.
- Concentric Circles
- Circles that share the same centre but have different radii.
- Chord
- A line segment connecting two points on the circumference of a circle; the diameter is the longest chord of a circle.
Frequently Asked Questions
What is the difference between congruence and similarity Class 8 Maths?▾
Congruent figures have the same shape AND the same size — one fits exactly on the other (like two identical coins). Similar figures have the same shape but can be different sizes — corresponding angles are equal and corresponding sides are in the same ratio (like a photo and its enlarged print). All congruent figures are similar, but not all similar figures are congruent.
What are the types of symmetry Class 8 NCERT?▾
Types of symmetry include: (1) Line symmetry (bilateral symmetry) — a line divides the figure into two mirror images; a square has 4 lines of symmetry, (2) Rotational symmetry — a figure looks the same after being rotated by a certain angle; a square has rotational symmetry of order 4 (looks same after every 90° rotation), (3) Point symmetry — the figure looks same from every direction through a central point.
What is a tessellation Class 8 Maths?▾
A tessellation is a pattern where shapes fit together to cover a surface with no gaps or overlaps. Regular polygons that can tessellate on their own are: equilateral triangles (interior angle 60°), squares (90°), and regular hexagons (120°) — because their interior angles are divisors of 360°. Other regular polygons cannot tessellate by themselves but can be combined.
What are geometric transformations Class 8?▾
Geometric transformations change the position or size of a figure: (1) Translation — sliding a figure in any direction without rotating, (2) Reflection — flipping a figure over a line of symmetry, (3) Rotation — turning a figure around a fixed point by a given angle, (4) Dilation — scaling a figure up or down (creating similar figures). The first three preserve size and shape (isometries); dilation changes size.
What are properties of circles Class 8 NCERT?▾
Key circle properties: (1) All radii of a circle are equal, (2) A diameter = 2 × radius, (3) The diameter is the longest chord, (4) A chord divides a circle into two parts (arcs), (5) The perpendicular from the centre to a chord bisects the chord, (6) Equal chords are equidistant from the centre, (7) Circumference = 2πr; Area = πr².
How are geometry and art related Class 8?▾
Geometry and art are deeply connected. Artists use symmetry, proportion, and geometric shapes to create beauty. Islamic art features complex geometric tessellations. Architecture relies on geometric principles for stability and aesthetics. Fractals (infinitely repeating geometric patterns) appear in nature (snowflakes, coastlines) and art. The golden ratio (approximately 1.618) appears in classical architecture and the human body.
Disclaimer & Attribution
- All NCERT textbook PDFs displayed on this page are served directly from NCERT's official servers at ncert.nic.in. We do not host, store, or redistribute any PDF files on our servers.
- This website is free to use. We do not sell, charge for, or commercially exploit any NCERT content.
- All textbook content is the intellectual property of NCERT, Government of India and is published under their open-access policy for educational purposes.
- This page is provided purely for educational reference in compliance with NCERT's guidelines for non-commercial use of their freely available materials.