Line Symmetry

Grade 2

What is a line of symmetry?

A line of symmetry divides a shape into two halves that are mirror images of each other. If you folded the shape along that line, the two halves would sit exactly on top of one another.

Not every shape has one. A scalene triangle has none. An equilateral triangle has three. A circle has infinitely many.

Lines of symmetry in common shapes

Square: 4 lines. Rectangle: 2 lines (horizontal and vertical only — the diagonals are not lines of symmetry). Regular hexagon: 6 lines. Isosceles triangle: 1 line. Kite: 1 line (the longer diagonal).

The diagonals of a rectangle are not lines of symmetry — folding along a diagonal gives a triangle, not the same shape. Diagonals of a square are lines of symmetry.

Using symmetry to find coordinates

EXAMPLE

Shape ABCD has a vertical line of symmetry at x = 3. Point A is at (1, 4). Find the coordinates of the mirror image of A.

Point A is 3 − 1 = 2 units to the left of the line x = 3. Its mirror is 2 units to the right: x = 3 + 2 = 5. The y-coordinate stays the same. Mirror of A = (5, 4).

Try this one

A square has both reflective and rotational symmetry.

(a) State the number of lines of symmetry and the order of rotational symmetry of a square. [2]

(b) A student claims that any shape with \( 4 \) lines of symmetry must have rotational symmetry of order \( 4 \). Explain, with reference to the square, why the order of rotational symmetry of a regular shape equals its number of lines of symmetry. [1]

Nova's hint:

Recall the symmetry of a square, then think about why the two kinds of symmetry match for regular shapes.

Ask yourself: 'how do the equally spaced mirror lines relate to equally spaced turning positions?' Consider that each mirror line and each rotation share the same centre and equal spacing.

Try to Solve it with Nova?