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
💡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 is 3 units to the left of a vertical mirror line. Where will its reflected image 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.