Multiline Symmetry

A Kite

There are two set squares in your instrument box; one has angles of measure 30°, 60°, 90°.

Take two such identical set-squares. Place them side by side to form a 'kite' shape as shown here.

How many lines of symmetry does this shape have?

Do you think that some shapes may have more than one line of symmetry?

(Illustration of a kite shape formed using two set squares, with a dotted symmetry line along its vertical axis.)

A Rectangle

Take a rectangular sheet (like a postcard). Fold it once lengthwise so that one half fits exactly over the other half.

Is this fold a line of symmetry? Why?

Open it up now and again fold along its width in the same way.

Is this second fold also a line of symmetry? Why?

Do you find that these two lines are the lines of symmetry?

Take a square piece of paper. Fold it into half vertically so that the edges coincide. Open the fold, and you will find that the two halves made by the fold are congruent. The fold at the centre becomes a line of symmetry for the paper. Try to fold the paper at different angles so that it becomes a line of symmetry.

How many folds are possible?

There are four lines of symmetry for a square.

(Illustrations:)

Square paper – A square shape.

Vertical fold – The square with a vertical dotted symmetry line.

Horizontal fold – The square with a horizontal dotted symmetry line.

Diagonal fold 1 – The square with one diagonal dotted symmetry line.

Diagonal fold 2 – The square with the other diagonal dotted symmetry line.

Opened appear – The square with all four symmetry lines intersecting at the center.

You can try drawing your own repeated patterns: