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.