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. Every Geometry class or course will include a deep exploration of the properties of parallelograms. Shoulder and arm tattoos by Micael Faccio on flicker. Royal Hawaiian officer via Wikimedia Commons.British Museum great court by Andrew Dunn, (Own work), via Wikimedia Commons ↵ Tile at Jerusalem temple by Andrew Shiva / Wikipedia, via Wikimedia Commons.Hexagonal and rhombic tessellations from Wikimedia Commons. Triangular tessellation from pixababy.Image by I, Xauxa, via Wikimedia Commons ↵.Circle and ellipse by Paris 16 (Own work), via Wikimedia Commons ↵.Head of a woman by Pablo Picasso, image from Gandalf's Gallery on flickr ↵ Pillar coral, wave, and molecule from Wikimedia commons.Normal distribution from Wikimedia Commons. Starfish by Paul Shaffner, via Wikimedia Commons. Butterfly by Bernard DUPONT from FRANCE (Swallowtail Butterfly (Papilio oribazus)), via Wikimedia Commons. Apollonian Circle Packing by Tomruen (Own work), via Wikimedia Commons. Mosaic image by MarcCooperUK (Flickr: Paris central mosque), via Wikimedia Commons.(You might want to visit and browse the “Symmetry” gallery.)Īnd it appears in traditional Hawaiian and other Polynesian tattoo designs. You can see translation symmetry in lots of places. The brick wall is one example of a tessellation, which you’ll learn more about in the next chapter. A brick wall has translational symmetry in lots of directions! A vector (a line segment with an arrow on one end) can be used to describe a translation, because the vector communicates both a distance (the length of the segment) and a direction (the direction the arrow points).Ī design has translational symmetry if you can perform a translation on it and the figure appears unchanged. Can you complete the design so that it has the correct rotational symmetry? Explain how you did it.Ī translation (also called a slide) involves moving a figure in a specific direction for a specific distance. Each picture below shows part of a design with a marked center of rotation and an angle of rotation given.