What is a Line of Symmetry in Geometric Shapes?

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  • 0:01 Geometric Shapes
  • 0:40 Lines of Symmetry
  • 1:32 Example: Rectangle
  • 2:03 Example: Letter A
  • 2:42 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After viewing this lesson, you should be able to identify shapes that have a line of symmetry in them and know how to find where this line is. A short quiz to test your knowledge will follow the lesson.

Geometric Shapes

In this lesson, we will talk about geometric shapes. Geometric shapes are, simply, shapes without any math attached to them. For example, if you see a circle drawn on a billboard, then you are looking at a geometric shape. If you see triangles, squares, octagons, or any other shape that you know, then you are looking at a geometric shape. Even curvy shapes are geometric shapes. The shape that the shadow of a dog makes is a geometric shape.

Yes, we see geometric shapes all around us. In this lesson, though, we are limiting the shapes that we are going to talk about. We are limiting them to the shapes that have a line of symmetry in them.

Lines of Symmetry

This line of symmetry is the line in the shape that splits the shape in half so that each half is the mirror image of the other. For example, the line of symmetry in a circle is one that cuts the circle in half and goes through the center of the circle. When you fold your circle along this line, you will find that the halves match up perfectly.

Geometric shapes can have more than one line of symmetry. How many does our circle have? A good way to find out is to start folding the circle in different ways. Remember, you want your halves to match up perfectly. How many different ways can you fold the circle so that the halves match up perfectly? You will find that a circle can be folded in many ways - actually, anywhere, as long as we go through the center of the circle. This tells us that the circle has an infinite number of lines of symmetry.

line of symmetry

Let's look at a couple more shapes and see about their lines of symmetry.

Example 1: Rectangle

Let's look at the rectangle. How can we fold the rectangle so that the halves match up perfectly? Well, we can fold it sideways in half. Can we fold it another way? Yes, we can. We can also fold it in half either going up or going down.

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