Symmetry and reflection

Hello, and welcome to Myriora Maths! Fold a butterfly picture down the middle, and both halves match exactly. That's symmetry! Let's find lines of symmetry, and reflect shapes in a mirror line.

A line of symmetry cuts a shape into two halves that are mirror images. If you fold along it, the halves fit exactly on top of each other.

Some shapes have more than one line of symmetry. A rectangle has two. A square has four. An equilateral triangle has three.

To reflect a shape in a mirror line, take each corner across the line. Count how far it is from the line, and go the same distance on the other side. Then join up the corners.

The reflection is the same size and shape, but it faces the other way. Every point is the same distance from the mirror line as its partner.

Let's try one together. How many lines of symmetry does a square have? Say it out loud!

Four! Two through the middles of the sides, and two through the corners.

Here's a question that catches lots of people. Does a rectangle have a line of symmetry from corner to corner? Some people say yes. But fold a rectangle along its diagonal, and the halves don't fit. A rectangle has only two lines of symmetry, through the middles of its sides.

Your turn! A point is two squares to the left of a mirror line. Where is its reflection? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! The reflection is the same distance on the other side. So it's two squares to the right of the line!

Quick review. A line of symmetry splits a shape into two matching halves. Some shapes have several lines of symmetry. To reflect a shape, take each corner the same distance to the other side of the mirror line. The reflection faces the other way. See you next time!