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Geometry - Lines of symmetry and reflection

Grade 4IGCSE

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

🔑Concepts

Line of Symmetry: An imaginary line that divides a shape into two identical parts that are mirror images of each other.

Reflective Symmetry: A shape has reflective symmetry if it can be folded along a line so that the two halves match exactly.

Mirror Line: The straight line where a reflection occurs. Every point on the original shape is the same distance from the mirror line as the corresponding point on the reflected image.

Horizontal and Vertical Symmetry: Lines of symmetry can go up and down (vertical), side to side (horizontal), or at an angle (diagonal).

Regular Polygons: Shapes where all sides and angles are equal. A regular polygon has the same number of lines of symmetry as it has sides (e.g., a square has 4).

📐Formulae

Number of lines of symmetry in a regular polygon=Number of sides\text{Number of lines of symmetry in a regular polygon} = \text{Number of sides}

Distance of Object from Mirror Line=Distance of Image from Mirror Line\text{Distance of Object from Mirror Line} = \text{Distance of Image from Mirror Line}

Orientation of Image=Laterally Inverted (flipped horizontally or vertically)\text{Orientation of Image} = \text{Laterally Inverted (flipped horizontally or vertically)}

💡Examples

Problem 1:

How many lines of symmetry does a non-square rectangle have?

Solution:

2 lines of symmetry.

Explanation:

A rectangle can be folded in half vertically and horizontally to match the sides perfectly. It cannot be folded diagonally because the corners will not meet.

Problem 2:

A point PP is 3 units to the left of a vertical mirror line. Where will its reflected image PP' be located?

Solution:

3 units to the right of the mirror line.

Explanation:

In reflection, the image is always the same distance from the mirror line as the original object, but on the opposite side.

Problem 3:

Which of these capital letters have at least one line of symmetry: A, F, H, L?

Solution:

A and H.

Explanation:

Letter 'A' has one vertical line of symmetry down the middle. Letter 'H' has two: one vertical and one horizontal. 'F' and 'L' cannot be folded to match perfectly.

Problem 4:

How many lines of symmetry does a regular pentagon have?

Solution:

5 lines of symmetry.

Explanation:

Since a regular pentagon has 5 equal sides and 5 equal angles, it follows the rule that the number of lines of symmetry equals the number of sides. Each line runs from a vertex to the midpoint of the opposite side.