MATHEMATICS Line Symmetry

Lesson Objectives The aim of this powerpoint is to help you… Review what we mean by ‘symmetry’ Draw reflections and find mirror lines Decide how many lines of symmetry something has

What is Symmetry? Give YOUR suggestions before we look at mine! Did you mention the words ‘balance’, ‘harmony’ or ‘equilibrium’? Symmetry is the quality of being made up of exactly similar parts either facing each other (as in reflective symmetry) or around an axis (as in rotational symmetry).

Types of Symmetry As mentioned in the definition, there are two types of symmetry. Reflective symmetry, also known as line symmetry, involves mirror images. Rotational symmetry involves turning about an axis.

Mirror Images Dependent upon which way your mirror is standing (or lying), mirror images become equal and opposites in some way. A vertical mirror changes lefts with rights and vice versa, but ups and downs remain the same. A horizontal mirror changes ups with downs and vice versa, but lefts and rights remain the same.

Line Symmetry - Reflections You may be given one side of the shape, the line of reflection (or mirror line) and asked to draw in the other side. You may be given the complete shape and asked to draw in the mirror line. This line is usually dotted and everything on the right (or above) needs to match up and balance with everything on the left (or beneath).

Drawing the other half… Given a vertical mirror line – remember lefts have to match up with rights. So positions 2 away on the right must be 2 away on the left and so forth… EXAMPLE: Here is half a shape and the mirror line. We need to draw the rest of the shape by drawing its reflection.

Drawing the other half… Starting from the top the shape goes: 2 left, 2 down, diagonal (2 down and to 2 left), diagonal (3 down and 2 right) then 2 right. Remember with a vertical mirror line, ups and downs remain the same but lefts become rights etc. From the top, the reflection will be: 2 right, 2 down, diagonal (2 down and to 2 right), diagonal (3 down and 2 left) then 2 left.

Drawing the other half… Given a horizontal mirror line – remember ups have to match up with downs. So positions 2 up above the line must match up with 2 down below the line and so forth… EXAMPLE: Here is half a shape and the mirror line. We need to draw the rest of the shape by drawing its reflection.

Drawing the other half… Starting from the left at the mirror line, the present shape goes: 4 up then 2 right, diagonal (3 down and to 2 right), 2 right then 1 up, 2 right then 2 down. Remember with a horizontal mirror line, lefts and rights remain the same but ups become downs etc. From the left, our reflection will be: 4 down then 2 right, diagonal (3 up and to 2 right), 2 right then 1 down, 2 right then 2 up.

Drawing the other half… Given a diagonal mirror line, distances on one side must equal distances on the other but all distances must be measured at right angles to the mirror line. I find the easiest thing is to tilt/turn the paper (or your head) so that the line becomes vertical or horizontal and then the reflection is much easier to draw.

Drawing the other half… If I tilt my head to the right, the line becomes vertical… … and from the top goes: diagonal (2 down, 3 left), diagonal (1 down, 1.5 right), diagonal (1 down, 1 left), diagonal (5 down, 1.5 right) Our reflection will (from top) be: diagonal (2 down, 3 right), diagonal (1 down, 1.5 left), diagonal (1 down, 1 right), diagonal (5 down, 1.5 left)

Drawing the Line of Reflection When drawing the line of reflection the key thing to remember is that IF there is a line of reflection, it must cut the shape or pattern exactly in half! Imagine the line cutting the shape in half and then check that the top matches the bottom or the right matches the left (or one diagonal matches the other)… It sometimes helps to imagine folding the image at the mirror line and checking that one half lies on top of the other half.

Drawing the Line of Reflection Here is a shape. Draw in the line(s) of reflection.

Drawing the Line of Reflection Let’s cut the shape in half in several ways and then check that one half folds over and matches the other: The purple lines show that there are NO matches! This is because a parallelogram has no reflective symmetry (only rotational symmetry).

Drawing the Line of Reflection Here is a shape. Draw in the line(s) of reflection.

Drawing the Line of Reflection Let’s cut the shape in half in several ways and then check that one half folds over and matches the other: The purple lines show that there are 2 matches! This is because a rectangle has 2 lines of symmetry.  

Small Group Task Please get into 2 groups. Each group will be given a different set of letters. TOGETHER, discuss and decide how many lines of symmetry each letter has. Once complete, designate one person in your group to present your solution to the other group. The solutions will appear on the next two slides so do NOT move on until after your presentations.

Mix’n’Match – Set 1 A C E G I KL O Q S U W Z

Mix’n’Match – Set 2 BD F H J MNP R T V X YV X Y

Notes and Examples In your exercise books or on paper, please write up your own notes and examples on line (or reflective) symmetry. It may help to include answers to the following questions… 1) What is symmetry? (You may look up a definition in a dictionary.) 2) What happens to reflections in vertical mirror lines? 3) What happens to reflections in horizontal mirror lines? 4) When mirror lines are diagonal, what is it best to do? What next? Move on to the next powerpoint presentation which is on rotational symmetry.