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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

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.

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.

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

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.

Can we fold it yet another way? Hmm, it doesn't look like it. If we tried to fold it diagonally, we'd find that the halves don't match up perfectly; they actually overlap in certain areas. What does this tell us? It tells us that a rectangle has two lines of symmetry.

Now, let's look at a more complicated shape. Let's look at the capital letter *A*. Does this geometric shape have a line of symmetry? Imagine folding it in different ways. Is there a way you can fold it in half so that the halves match up perfectly? Yes, there is. Which way is this? If you fold it in half sideways, you will see that both halves will match up perfectly. Is there another way? No. So, the capital letter *A* has one line of symmetry.

There are many other shapes that have lines of symmetry. Start folding and you will discover more of them.

Let's review what we've learned. We learned that **geometric shapes** are simply shapes without any math attached to them. A **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.

A geometric shape can have more than one line of symmetry. A circle, for example, has an infinite number of lines of symmetry. To find lines of symmetry, fold your shape in half in different ways. When your shape folds in half and the halves match up perfectly, you have found a line of symmetry.

After you finish this lesson, you should have the ability to:

- Explain what geometric shapes are
- Define line of symmetry
- Utilize examples to figure out lines of symmetry

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- What is a Line of Symmetry in Geometric Shapes? 3:19
- Similarity in Geometric Shapes 6:03
- Parallel, Perpendicular and Transverse Lines 6:06
- Identifying Parallel Lines in Geometric Shapes 3:35
- Constructing Perpendicular Lines in Geometry 3:39
- Identifying Perpendicular Lines in Geometric Shapes 3:54
- What is Symmetry in Math? - Definition & Concept 2:54
- Go to 6th-8th Grade Geometry: Symmetry, Similarity & Congruence

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