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Tamil Nadu (TNBSE)Class 3 Mathematics★ 5-6 marks across TN Class 3 exams — 2D/3D shape properties, perimeter introduction, symmetry, and tessellation

Geometry

Samacheer Kalvi (TN State Board) Class 3 Mathematics — Chapter 1, Geometry. Shapes, angles and lines of symmetry. Study notes, key concepts, worked examples, practice questions and quick revision for exam preparation.

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By the end of this chapter you'll be able to…

1Name polygons by number of sides: triangle (3), quadrilateral (4 — square, rectangle), pentagon (5), hexagon (6)
2Count sides and corners (vertices) of any polygon
3Identify and draw a line of symmetry in 2D shapes, letters (A, M, T), and everyday objects
4Calculate perimeter of simple 2D shapes by adding all side lengths (e.g., rectangle: 2 × (length + breadth))
5Identify shapes that tessellate (triangle, square, rectangle, hexagon) and those that don't (circle, pentagon)
6Identify 3D shapes and count faces, edges, and vertices: cube (6 faces, 12 edges, 8 vertices), cuboid, cylinder, cone, sphere

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Why this chapter matters

Class 3 geometry transforms children from shape identifiers to shape analysts. They learn to count sides and corners of polygons, identify and draw lines of symmetry, calculate perimeter by adding side lengths, and understand tessellation — how shapes fit together without gaps (like floor tiles). Symmetry is particularly important: it connects geometry to art, nature (butterfly wings, leaves), and Tamil cultural motifs like kolam designs. A kolam is mathematics made beautiful — rotational and reflectional symmetry drawn in rice flour every morning.

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Geometry — Class 3 Mathematics (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 3 Mathematics, Chapter 1. Shapes, angles and lines of symmetry.

1. About this chapter

This chapter covers Geometry as part of the Class 3 Samacheer Kalvi Mathematics curriculum. It deals with shapes, angles and lines of symmetry and builds conceptual understanding essential for the TN School Term Exam.

By the end of this chapter, students will be able to:

Identify 2D and 3D shapes
Recognise lines of symmetry

2. Key concepts

Concept 1: Identify 2D and 3D shapes.
Concept 2: Recognise lines of symmetry.

3. Important terms and formulas

Term / Formula	Description
Identify 2D and 3D…	Identify 2D and 3D shapes
Recognise lines of symmetry…	Recognise lines of symmetry

4. Worked examples

Example 1. Applying a key concept from this chapter.

Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.

Example 2. A typical exam-style question on geometry.

Solution: Break the problem into steps, use the appropriate formula and verify the answer.

5. Common mistakes

Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.

6. Practice (exam-style)

Define the main term or principle covered in Chapter 1.
Give two real-life examples related to geometry.
Solve a short numerical or descriptive question from this chapter.
State one important formula and explain each symbol.

7. Answer key (hints)

Refer to section 2 (Key concepts) above for the definition.
Examples should be drawn from daily experience and local context.
Apply the formula from section 3, show all steps clearly.
Formula with units — refer to the textbook glossary for symbol meanings.

8. Quick revision

Class 3 Mathematics — Chapter 1: Geometry.
Core idea: Shapes, angles and lines of symmetry.
Key outcomes: Identify 2D and 3D shapes; Recognise lines of symmetry.
Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Perimeter

Perimeter = sum of all sides. Square: P = 4 × side. Rectangle: P = 2 × (length + breadth). Triangle: P = side1 + side2 + side3.

Perimeter is the distance AROUND a shape — like walking along the boundary fence of a park. If a rectangular playground is 30 m by 20 m, the perimeter = 2×(30+20) = 100 m.

Symmetry

A line of symmetry divides a shape into two identical halves that are mirror images. One fold — both halves match exactly. Shapes: square has 4 lines of symmetry, rectangle 2, equilateral triangle 3, circle infinite. Letters: A (1 vertical), M (1 vertical), T (1 vertical), H (2 — vertical and horizontal).

Kolam (rangoli) designs drawn in Tamil Nadu every morning are masterpieces of symmetry. The dots are placed in a grid, and lines are drawn around them — often with rotational and reflectional symmetry.

Tessellation

A tessellation (tiling) covers a surface with shapes that fit together with NO gaps and NO overlaps. Shapes that tessellate: equilateral triangle, square, rectangle, regular hexagon. Shapes that do NOT tessellate alone: circle (gaps), regular pentagon (gaps).

Look at the floor tiles in your house or school — they are usually squares or rectangles that tessellate perfectly. A honeycomb is nature's tessellation — hexagons fit together with zero wasted space.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Counting the diagonal of a rectangle as a line of symmetry

✓ Folding a rectangle along its diagonal does NOT produce matching halves — try it with paper. A rectangle has exactly 2 lines of symmetry: one vertical through the middle, one horizontal through the middle.

WATCH OUT

✗ Confusing perimeter (distance around) with area (space inside)

✓ Perimeter = distance you WALK around the edge. Area = space INSIDE the boundary. At Class 3, focus is on perimeter. Area comes in Class 4-5.

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