Lesson 21 — Activity 1: Sorting Quadrilaterals According to Symmetry


Getting Ready


Symmetry means that you can divide an object in such a way so that each part of the divided object is a mirror image of the other part. A line of symmetry is the place that you can divide an object so that both sides are mirror images of each other.

This image shows you an example of symmetry.

If you have a square piece of paper and fold it in half so that you have a triangle shape, the fold line is a line of symmetry. Both sides of the fold are mirror images of each other.


If you look at the shape below, you will notice that it has four dotted lines. Each line is a way that you can fold a square so that each part is a mirror image of the other part. 


Count the number of dotted lines to see how many lines of symmetry a shape has.

So as you can see, a square has four lines of symmetry.



You can use lines of symmetry to classify different quadrilaterals. Remember that a quadrilateral is any 4-sided shape. Some have no lines of symmetry while others have many lines of symmetry.

Let's look at a few quadrilaterals. Look at the dotted lines to find the lines of symmetry. Can you see that both sides are equal?


A rhombus has two lines of symmetry.


Lines of symmetry on a rhombus

A rectangle has two lines of symmetry.


Lines of symmetry on a rectangle

An isosceles trapezoid has one line of symmetry.


Lines of symmetry on an isosceles trapezoid

An asymmetrical kite has no lines (or "zero") of symmetry.


Lines of symmetry on an isosceles trapezoid