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Fun with Symmetry

Counting lines of symmetry

Count the lines of symmetry in different shapes.

In your book, Maths Mela (Chapter 11), there are shapes drawn on squared grids: six triangles and eight shapes with four sides. A triangle always has 3 sides. A shape with 4 sides is called a quadrilateral. The book asks how many lines of symmetry each shape has. You can trace a shape and fold it to check: a fold where the two halves match exactly is a line of symmetry.

A square has 4 lines of symmetry: one up and down, one across, and one along each diagonal, from corner to corner. A rectangle that is not a square has only 2: up and down, and across. If you fold a rectangle from corner to corner, the halves do not match. A rhombus (a diamond shape with 4 equal sides, but not a square) also has 2, along its two diagonals.

Some shapes have just 1 line of symmetry: a kite, a trapezium whose two slanting sides are equal, and an arrowhead. A triangle with exactly two equal sides (the third side different) also has 1, down its middle.

Some shapes have none at all: 0 lines of symmetry. A triangle with no equal sides has 0. A slanting parallelogram (like a rectangle pushed over) also has 0: no fold makes its halves match.

A square has 4 lines of symmetry, a rectangle and a rhombus 2, a kite, an arrowhead and a triangle with two equal sides 1, and a slanting parallelogram 0.

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