Basic Mathematics Review 5232

Basic Mathematics Review 5232 Symmetry A geometric figure has a line of symmetry if you can draw a line so that if you fold your paper along the line the two sides of the figure coincide. In other words, a shape has a line of symmetry if one half of it is the mirror image of the other half. Line of Symmetry Fold Line Mirror Mirror When you fold a shape along a line of symmetry, one half fits exactly over the other. These are examples of symmetry: When you put a mirror on a line of symmetry and look from either side, the shape looks like the original. These are not examples of symmetry: Objective Review 5232 1

Review 5232 Basic Mathematics Example: Does a rectangle have any lines of symmetry? A rectangle has two lines of symmetry. Example: Let us look at a square. How many lines of symmetry can we find in a square? A square has the same two lines of symmetry as the rectangle in the first example. Additionally, the square has two more lines of symmetry as shown in the figure below. In total, a square has four lines of symmetry Objective Review 5232 2

Basic Mathematics Review 5232 Example: Let us look at a circle. How many lines of symmetry can we find in a circle? Notice that if we draw a line through the center of the circle, we can fold the figure along that line and the two sides of the circle coincide. A line through the center of a circle is called a diameter. In fact, we can draw an infinite number of lines through the center of a circle; therefore, we can see that a circle has an infinite number of lines of symmetry Example: Let us look at a parallelogram. How many lines of symmetry can we find in a parallelogram? Notice that if we draw a horizontal line through the center of the parallelogram, and fold the figure along that line, the two sides of the parallelogram do not coincide. If we draw a vertical line through the center of the parallelogram and fold the figure alone that line, we can see that the two sides do not coincide. In addition, if we draw diagonals on the parallelogram and folded along the diagonal, we can see that the parallelogram is not symmetric. In fact, we can see that a parallelogram has no lines of symmetry. Objective Review 5232 3

Review 5232 Basic Mathematics Example: How many lines of symmetry can we find in a pentagon? Notice that if we draw a line through the center of the pentagon, we can fold the figure along that line and the two halves coincide. In fact, we can draw a number of lines through the vertices and the opposite sides of a regular pentagon; therefore, we can see that the pentagon has 5 lines of symmetry. Objective Review 5232 4

Basic Mathematics Review 5232 Lines of Symmetry in Regular Polygons Polygon Sides Internal Angles Lines of Symmetry Triangle 3 3 3 Square 4 4 4 Pentagon 5 5 5 Circle Infinite Infinite Infinite Objective Review 5232 5

Review 5232 Basic Mathematics Rotational Symmetry Another type of symmetry is rotational symmetry. An image has rotational symmetry if there is a center point around which the object is turned a certain number of degrees and the object still looks the same. In other words, it matches itself a number of times while it is being rotated. Example: Let us look at an equilateral triangle. Is there a way we can turn this triangle and have a triangle of the exact look, position, and orientation? 120º Notice that if we rotate the triangle 120º, the look, position, and orientation are the same. Therefore, we can say that the equilateral triangle has rotational symmetry of 120º. Example: Let us look at a rectangle. Does a rectangle have rotational symmetry? 90º 180º Notice that if rotate the rectangle 90º, the position and orientation are not the same, but if we rotate the rectangle another 90º, the position and orientation are exactly the same. All rectangles have rotational symmetry of180º. Objective Review 5232 6

Example: Does a square have rotational symmetry? Basic Mathematics Review 5232 90º Notice that if we rotate the square 90º, the position and orientation are the same. Therefore, we can say that the square has rotational symmetry of 90º. Real Life Examples Many animals and plants and other things in nature have lines of symmetry or rotational symmetry. Objective Review 5232 7