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# How do you find lines of reflective symmetry? (Taj Mahal India is a famous building with reflective symmetry)

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A line of a reflective symmetry can be placed through a shape so that one side of the shape is a mirror image of the other side of the shape. A good method to decide if a shape has reflective symmetry is to draw the shape out on paper and cut it out. If you can fold the shape along the line of symmetry so that the two halves fit together perfectly then you have found a line of symmetry. Alternatively, you could use a small rectangular mirror to help you out (or tracing paper). A line of symmetry is marked with a dashed line (although it is acceptable to draw a normal line).

Reflectional symmetry occurs in nature and in many famous building around the world, one such being the Taj Mahal in India.

Example

How many lines of symmetry does a rectangle have?

A rectangle has 2 lines of symmetry (a horizontal and vertical line)

Example 2

How many lines of symmetry does a square have?

A square has more lines of symmetry than a rectangle. It also has diagonal lines of symmetry, as well as the vertical and horizontal lines of symmetry.

So in total a square has 4 lines of symmetry.

Example 3

How many lines of symmetry does a parallelogram have?

You need to be careful with a parallelogram. It has 0 lines of symmetry (cut it out and fold it up if you still think there are more than 0!).

Example 4

How many lines of symmetry does an equilateral triangle have?

Again, be careful with an equilateral triangle. An equilateral triangle has 3 lines of symmetry. You should be able to see the diagonal ones by turning the shape around.

Example 5

Out of the letters A, C, H, J, M, O, X and Y which letters have exactly one line of symmetry?

The letter A has 1 vertical line of reflective symmetry.

The letter C has 1 horizontal line of symmetry.

The letter H has 2 lines of symmetry (vertical and horizontal)

The letter J has no lines of symmetry.

The letter M has 1 vertical line of symmetry.

The letter O has an infinite number of lines of symmetry.

The letter X has 4 lines of symmetry.

The letter Y has one line of vertical symmetry.

So the letter with 1 line of symmetry are A,C, M and Y.