Have you ever wondered how many lines of symmetry a hexagon has? Does it have 4, 6, or 8? How can you find the lines of symmetry in a hexagon? Do all hexagons have 6 lines of symmetry? How do you draw a line of symmetry for a hexagon? In this blog post, we will answer these questions and more.
The first question, How many lines of symmetry do a hexagon have? is actually not as simple as you might think. A hexagon has three pairs of parallel sides with opposite angles at each end (a total of six). However, it also can be seen that the points where these edges meet form another pair perpendicular to those on the ends. So technically there are four sets of adjacent and non-overlapping sets forming a line which makes for five possible lines in all. This leads us to our next point:
Do all hexagons have six lines of symmetry?
The answer is no! If we only counted those segments that were part of two different triangles then we would see less than the full six lines because if one triangle is created by two sets of parallel sides then it is impossible for the other to be made up from those same segments.
It’s important to note that a line of symmetry in any shape can only pass through edges and not interior points, so we need at least three points on our hexagon before we draw lines of symmetry.
But let’s say you want to find all possible ways your hexagon could have six lines? It would involve tracing out every triangle within your hexagon with your pencil and seeing if there were more than one edge that formed another triangle (a line). We will give an example below:
The yellow areas are all triangles being traced out while red X’s represent where new ones might form as soon as we trace out the edges. Every time you find a new line of symmetry (marked with red X) from one end to another, mark it on your hexagon and then start tracing triangles in that area until you either run into an edge or come back around to where you started. Repeat this process for all six areas of symmetry so there are as many lines as possible.
If our hexagon has two sets of parallel sides then it is impossible for the other set to be made up from those same segments. It’s important to note that a line of symmetry in any shape can only pass through edges and not interior points, so we need at least three points before drawing lines of symmetry but let’s say I want to draw lines of symmetry through the point at which two other edges meet. If I do this and then try to find points for a second line, it will never work out because no matter what order we trace in or how many times we rotate around one set of axes, the first line is always going to be coming back from where it started while that’s not true with any subsequent ones.
Lastly, if you’re drawing your hexagon on graph paper with its sides numbered so that when we identify an edge by number (e.g., A) instead of the letter (A), they are opposite numbers on either side of zero, then every time you come across another edge being marked as ‘0’, just add six more zeros before it to get the number of that edge. When you do this, every side will correspond with a unique whole number (0, 0 12, 00 18) and any time two lines intersect each other on your hexagon drawing they’ll create a point at which three edges meet since their adjacent numbers are always opposite one another.