Learn about Bilateral and Rotational Symmetry Bilateral and Rotational Symmetry In this problem, we need to determine whether each figure has bilateral symmetry. Is the line of symmetry the same as the above? For the first one, we need to determine whether each figure has bilateral symmetry. You can fold the figure to find out if it is symmetrical. When you find if something has symmetry, you fold it just like if would fold a piece of paper. This fold line is called the line of symmetry. The figure has bilateral symmetry when if when you fold it, one side fits exactly over the other side, so it has bilateral symmetry when if you fold it, one side fits exactly over the other side. Let’s take a look at A. Here we have a smiley face and we have the line of symmetry, so this would be the line of symmetry. This is our fold line. The two parts of the figure match exactly. They match exactly when you fold or reflected across this line of symmetry, so this figure has bilateral symmetry and the line shown is its line of symmetry. Let’s take a look at this second part B. The two parts of this figure do not match exactly when folded or reflected across this line. So, this line is not the line of symmetry because if you were to fold this over, they would not meet exactly. Now, please note that this figure is a rectangle. So, here we have a rectangle. A rectangle does have bilateral symmetry across a vertical line through its center. So, if you would have a rectangle, it has a bilateral symmetry across the vertical line through the center. So, if I were to make a line down the center, this dotted line shows the line of symmetry, so it does have a bilateral symmetry and this line would be the line of symmetry. However, in this figure, this is not the line of symmetry nor does this have bilateral symmetry. Let’s move on to the second part. Here, we need to tell whether each figure has rotational symmetry. If a figure will fit exactly over itself after being rotated clockwise or counterclockwise, a 180 degrees or less, it has rotational symmetry. Let’s look at this first figure and let’s determine if this first figure has rotational symmetry. If were to look at this figure, when this figure is rotated 180 degrees, so we rotate it, turn it once and then twice, 180 degrees or less, it looks as it did before it was rotated. So, anytime you rotate this figure, it looks the same. It looks the same as it did before you rotate it. So, that means this figure has rotational symmetry. Let’s take a look at this second figure B, the smiley face. If were to rotate this face. If we were to rotate this smiley face a 100 degrees or less, so 90 degrees or 180 degrees, it does not look as it did before it was rotated. So, if you notice as you rotate it, these two figures don’t look the same. If rotate it again, they don’t look the same. So, that means this figure does not have rotational symmetry. Things to remember and keep in mind, you can hold the figure to find out if it’s symmetrical and the fold line is the line of symmetry. The figure has bilateral symmetry if when you fold it, one side fits exactly over the other side. If a figure will fit exactly over itself after being rotated clockwise or counterclockwise, 180 degrees or less then the figure has rotational symmetry.