Or spending way too much time at the gym or playing on my phone. You can often find me happily developing animated math lessons to share on my YouTube channel. (Never miss a Mashup Math blog-click here to get our weekly newsletter!)Īnthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's ' With Math I Can ' Campaign. Share your thoughts, questions, and suggestions in the comments section below! However, even though parallelograms do not have line symmetry, they do have rotational symmetry since any parallelogram, after a rotation of 180 degrees, will result in the exact same image as you started with. Parallelograms have zero lines of symmetry because it is impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other. In today’s lesson, we explored parallelogram lines of symmetry, whether or not they exist, and whether or not parallelograms have any symmetry at all.Īfter reviewing the properties of parallelograms, namely that they are quadrilaterals where the opposite sides and opposite angles are equal, we went on to determine whether or not parallelograms have any line symmetry.īy applying the definition of a line of symmetry, we concluded that, while shapes like squares and rectangles do indeed have lines of symmetry, that parallelograms do not have any lines of symmetry. In the diagram below, you can see that a square has four lines of symmetry, while a rectangle and a rhombus each have only two lines of symmetry. In fact, a shape can have multiple lines of symmetry. If parallelograms do not have lines of symmetry, then why doesn’t a parallelogram have lines of symmetry?įor starters, let's note that a line of symmetry is an axis or imaginary line that can pass through the center of a shape (facing in any direction) such that it cuts the shape into two equal halves that are mirror images of each other.įor example, a square, a rectangle, and a rhombus all have line symmetry because at least one imaginary line can be drawn through the center of the shape that cuts it into two equal halves that are mirror images of each other. What is the number of lines of symmetry in a parallelogram? Now that you understand the key properties and angle relationships of parallelograms, you are ready to explore the following questions: The following diagram illustrates these key properties of parallelograms: And any pair of adjacent interior angles in a parallelogram are supplementary (they have a sum of 180 degrees). And, if a parallelogram has line symmetry, what would parallelogram lines of symmetry look like (in the form of a diagram).īefore we answer these key questions related to the symmetry of parallelograms, lets do a quick review of the properties of parallelograms: What is a parallelogram?ĭefinition: A parallelogram is a special kind of quadrilateral (a closed four-sided figure) where opposite sides are parallel to each other and have equal length.įurthermore, the interior opposite angles in any parallelogram have equal value. In this post, we will quickly review the key properties of parallelograms including their sides, angles, and corresponding relationships.įinally, we will determine whether or not a parallelogram has line symmetry. Which of the following has the most lines of symmetry? The square.Every Geometry class or course will include a deep exploration of the properties of parallelograms. That means the square has the two lines of symmetry that all rectangles have plus two more, each diagonal. They can also be divided in half diagonally. But there’s something special about squares. Just like the rectangle, they can be divided in half this way and this way. We know that squares are one type of rectangle. We can fold the rectangle in half this way or this way, giving the rectangle two lines of symmetry. This equilateral triangle and in fact all equilateral triangles have three lines of symmetry. A square has 4 lines of symmetry, a parallelogram has no lines of symmetry, and a rectangle has 2 lines of symmetry. And finally, a third line of symmetry for equilateral triangles. Here is another line of symmetry for an equilateral triangle. If you folded the triangle at this line, both halves are equal. Remember that our lines of symmetry are the places where one-half of our shape is reflected to the other half. To determine which shape has the most lines of symmetry, we’ll need to find out how many lines of symmetry is in each shape. Why don’t we start by sketching each of these shapes? First, an equilateral triangle, a triangle where all three sides are the same length. Which of the following has the most lines of symmetry - equilateral triangle, rectangle, or square?
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