![]() In other words, ∠1 has a measure of 60° also. We know that lines l and m are parallel and crossed by transversal n, so alternate interior angles are congruent. First, we can extend these side lengths to better see the parallel lines at play here. Even if we don't know much about hexagons, we sure know about parallel lines and transversals, so let's use what we know. Since it's a regular hexagon (six-sided polygon), we know it's made up of sets of parallel lines. ![]() What is the total measure of all interior angles of this regular hexagon? Seeing these relationships among segments and angles makes it possible to find angle measures and side lengths in polygons. If we take another look at the perpendicular lines, we'll see that we have four sets of parallel lines here as well: a || d, b || g, c || f, and e || h. If two lines are perpendicular to the same line, we know that they're parallel. So perpendicular lines managed to sneak their way into shapes that don't even have 90° angles. Just the same, lines c and f are perpendicular to b and g. We can see that lines a and d are perpendicular to both e and h. If we extend the sides out, we can see clearly how the segments are related to each other. How many sets of parallel and perpendicular lines are there in a regular octagon?Ī regular octagon is made up of eight sides of the same length, and eight congruent angles (all of which measure 135°). A regular pentagon has no parallel or perpendicular sides, but a non-regular pentagon might have parallel and perpendicular sides. Lots of polygons will have no parallel or perpendicular sides, but some will have some.Īs we mentioned before, right triangles have perpendicular sides, rectangles have both perpendicular and parallel sides, but other quadrilaterals might not. Sample Problemĭo non-regular polygons have parallel or perpendicular sides? Parallel lines are equally popular, since every regular polygon with an even number of sides is made up of sets of parallel line segments. Rectangles, right trapezoids, and loads of other polygons have perpendicular line segments (including right triangles, which are special enough to have an entire chapter named after them). Many polygons have parallel and perpendicular sides. Squares are made up of two sets of parallel line segments, and their four 90° angles mean that those segments also happen to be perpendicular to one another. But what do they have to do with parallel and perpendicular lines? Parallel and Perpendicular Lines in Polygonsįine, polygons are everywhere.You already know this stuff, so we won't bore you with it. Triangles have 3 sides, quadrilaterals have 4, pentagons have 5, hexagons have 6, and so on. ![]() If we need to get more specific with describing polygons, we usually do so by the number of sides they have. Seriously, it's illegal not to, and traffic school ain't all it's cracked up to be. Don't forget to stop by and say hello when you pass it. We've seen regular polygons all our lives, from that triangle in music class, to the friendly red octagon around the corner. For any shape that has more than 4 sides, just put "regular" in front of the name (regular pentagon, regular hexagon, etc.) to indicate that it has routine bowel movements. Regular polygons include shapes like equilateral triangles and squares. If polygons have sides that are all equal in length, angles that are all equal in measure, and daily trips to the loo, we call them regular. Of course, that last one isn't specific to mathematicians. There are two things mathematicians simply can't stand: uncertainty and waiting in line at the DMV. Can you figure out why?Įven splitting up shapes into categories like "polygon" and "non-polygon" leaves a lot of room for uncertainty. Triangles, squares, rectangles, pentagons, and other more complicated shapes like the ones below are all examples of polygons. In order to be a polygon, a shape must be: A polygon is a closed two-dimensional shape that's made up of only straight line segments.
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