How to find Symmetry | Geometry Review
What happens when I take these two shapes, and I split them in half? The shapes are identical in size and shape right? I can see this more clearly by folding the images on top of each other.
So, we can see that when I have drawn a line, I have created two congruent shapes. Congruent means that the two shapes are identical. When you are able to draw a straight line through the center of a shape, and it creates two congruent shapes, then these two shapes are also symmetrical.
Symmetry comes from the Greek word Symmetria meaning “a similar agreement of parts.”
Symmetry, just like congruent shapes, means that one shape becomes exactly like the other when you move it in some way. This movement could be a turn, a flip, or a slide.
When a shape is not symmetrical, then this is referred to as asymmetrical.
Some shapes have lines of symmetry. A line of symmetry is a line that splits the shape in half, creating an identical shape. Some shapes only have one line of symmetry, some have two, and some have several!
However, to draw a line of symmetry, we must first identify the point of symmetry. This is because the point of symmetry marks the point that the lines of symmetry would pass through.
A point of symmetry is when there is a position or central point on an object or shape where the central point splits the object into two identical parts. And, every single line and angle on the other side of the central point is the same exact distance from the central point on each side.
That was a lot. Let’s take a look at what I mean.
For example a cross. Where both identical lines of the cross intersect, we can see that there is a point of symmetry, but let’s take a look at the definition to make sure.
Does the point split the cross into two identical, or congruent, parts?
Is every single line or angle of the ‘x’ the exact same distance from the central point on each side?
Based on what we can see, it definitely appears that way. However, to be one hundred percent sure, we would need to measure every single line and angle. But, for this exercise, I have used an example where all the lines and angles are the exact same distance, so check!
Now, let’s practice finding lines of symmetry.
Since, we have already found the point of symmetry on the cross, let’s see how many lines of symmetry it has. How many times can we split the cross, and get identical parts?
1, 2, 3, 4. After 4, there are no other lines that would give us two identical parts.
Great job guys!
Let’s try another.
How many lines of symmetry does the dog have? Or how many lines can you draw that create multiple identical parts?
Just one. If there were any more lines, then we would not have identical parts.
What about the side of the dog? Do you see any lines of symmetry?
No. Each end of the dog has differently shaped parts. The head is different than the tail.
What about this thought bubble? Is there a line you can draw to create two identical parts? No.
Any line you draw creates two differently shaped parts.
Let’s try one more.
How many lines of symmetry does this hexagon have?
Let’s see how many lines we can draw to split this hexagon into identical parts.
You guys have done a really great job.
Keep practicing be looking for shapes that are symmetrical in your classroom, in your house, outside, or wherever you are.
Symmetry is everywhere, and it’s very important. Architects and engineers use symmetry to design sturdy buildings, and other objects. Interior designers use symmetry, and asymmetrical designs to make their work more appealing to look at. People everywhere use symmetry in some way.
I hope this video was helpful. Be sure to check out our other videos for further questions.
See you next time.