![]() A quadrilateral is a four‐sided polygon.The following lists the different types of polygons and the number of sides that they have: Polygons are also classified by how many sides (or angles) they have. Segments QS, SU, UR, RT and QT are the diagonals in this polygon. Sides AB and BC are examples of consecutive sides.įigure 2 There are four pairs of consecutive sides in this polygon.Ī diagonal of a polygon is any segment that joins two nonconsecutive vertices. It does not matter with which letter you begin as long as the vertices are named consecutively. The four‐sided polygon in Figure could have been named ABCD, BCDA, or ADCB, for example. When naming a polygon, its vertices are named in consecutive order either clockwise or counterclockwise.Ĭonsecutive sides are two sides that have an endpoint in common. The endpoints of the sides of polygons are called vertices. ![]() Figure 1 shows some convex polygons, some non‐convex polygons, and some figures that are not even classified as polygons.įigure 1 Which are polygons? Which of the polygons are convex? Polygons first fit into two general categories- convex and not convex (sometimes called concave). The term polygon is derived from a Greek word meaning “many‐angled.” In this definition, you consider closed as an undefined term. Alternatively, a polygon can be defined as a closed planar figure that is the union of a finite number of line segments. Summary of Coordinate Geometry FormulasĬlosed shapes or figures in a plane with three or more sides are called polygons.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.Remember when you're asked that on your true and false questions, the key things about polygons are closed figure, three sides, none of which are curved, and you classify it by how many sides it has. So when you're naming a polygon, pick any vertex and go in a consecutive order, either counter clockwise or clockwise. So I could say this is D, E, A, B, and C. The other one, if I'm starting with D, is to go in the opposite direction. ![]() I can go D, C, then B, then A, and then E. So if I start with D, there are two ways that I can name this pentagon. If I start with D, I can go in, clockwise or counter clockwise, but going to have to be consecutive. Well that's pretty easy because all you have to do is pick one vertex. Now the last key thing about polygons is how do you name them. But you only need one to be considered concave. It just so happens that we have two in this polygon. So here, I can draw in a diagonal that is not within this polygon. To be concave, you need at least one diagonal that is outside of your polygon. So in this polygon, if I drew in my diagonals, you'll notice that all of those diagonals are contained within that polygon. Remember a diagonal is a segment that connects non consecutive vertices. Now there are two different types of polygons, convex and concave. This is something that you're going to have to memorize because you're going to see it on tests and quizzes throughout geometry. So what you're going to need to do is memorize a table, that's probably found in your textbooks, that lists the number of sides and the name for that polygon. This would not be a polygon because, yes three are the lines are straight, but you have one curved side, so this would not be a polygon.Īnd the third thing is that they're classified by the number of sides. So if we go back to this figure I drew originally, and let's say instead of drawing a straight line, I drew some sort of curved line. If you have less than three, you can't close any figure. The second thing about polygons is that it has at least three sides. However, if I drew in a line segment then it would be a polygon because now it is closed. So if I drew a figure down here, this would not be a polygon because as you can see, there's this open space here. First of all, a polygon is a closed figure. Polygons are discussed throughout Geometry, so it's important to know their characteristics.
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