13.03 Line and rotational symmetries

Can you identify  lines of symmetry  in a shape? Look at the picture of a dog house below, is it symmetrical? Could you place a line through the picture so that the image on one side matches the image on the other?

If you can fold or cut a shape in half, and both sides look identical, we can say that shape has line symmetry. Let's learn more.

Examples

Example 1

How many lines of symmetry does this painting have?

Worked Solution

Create a strategy

Think of how many different lines can be drawn to split an object into two identical halves.

Apply the idea

Here is one of the lines of symmetry.

Lines of symmetry can also be drawn horizontally, vertically, and diagonally the other way.

So there are 4 lines of symmetry.

Watch question walkthrough

If you can spin or turn a shape or object part the way around, and it looks identical, we can say the shape has rotational video. Watch this video to learn more.

Examples

Example 2

Which of the following shapes have rotational symmetry?

A

B

C

D

Worked Solution

Create a strategy

Imagine rotating the shape and see if it perfectly overlaps the original shape after a rotation that is less than 360\degree.

Apply the idea

Among the choices, the rectangle has rotational symmetry at 180\degree and 360\degree.

So, the correct answer is Option A.