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Geometry - Symmetry in 2D shapes

Grade 3IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Definition of Symmetry: A shape has symmetry if it can be folded or divided into two identical halves that match exactly.

Line of Symmetry: The 'fold line' or imaginary line that divides a shape into two mirror-image parts.

Vertical Symmetry: A line of symmetry that runs up and down (e.g., the letter 'A').

Horizontal Symmetry: A line of symmetry that runs from left to right (e.g., the letter 'E').

Regular Polygons: Shapes with all sides and angles equal (like a square) have multiple lines of symmetry.

Mirror Image: One side of a symmetrical shape is the reflection of the other side.

📐Formulae

Rule for Regular Polygons: Number of lines of symmetry = Number of sides (e.g., a regular pentagon has 5 lines of symmetry).

Congruency Rule: The two parts created by a line of symmetry must be congruent (identical in shape and size).

💡Examples

Problem 1:

How many lines of symmetry does a square have?

Solution:

4 lines of symmetry.

Explanation:

A square can be folded vertically (1), horizontally (1), and diagonally from both sets of corners (2), making a total of 4 lines.

Problem 2:

Does the letter 'M' have a vertical or horizontal line of symmetry?

Solution:

Vertical line of symmetry.

Explanation:

If you draw a line straight down the middle of the 'M', the left side is a mirror image of the right side.

Problem 3:

Which shape has more lines of symmetry: a rectangle or a circle?

Solution:

A circle.

Explanation:

A rectangle has only 2 lines of symmetry (vertical and horizontal). A circle has an infinite (unlimited) number of lines of symmetry because any line passing through its center divides it into two equal halves.