The triangles each have a total of 180°, so the total for the three triangles is 540°. The angles of the pentagon are split up, but adding up the angles of all the triangles will make up the angles of the pentagon. In this pentagon, drawing all the possible diagonals from one vertex divides the pentagon into three triangles. If you draw all the diagonals from one vertex, you break the polygon up into triangles. A quadrilateral can be split into two triangles by drawing one diagonal, and you can see that the total of the measurements of the four angles in a quadrilateral is 360°. The sum of the measures of the three angles of a triangle is 180°. If a polygon has n sides, it will have diagonals. Six times three is 18, divided by two is nine diagonals in a hexagon. The hexagon has six starting places and three ending places, but again you have to divide by two because of the duplicates. In fact, there are only five diagonals in a pentagon because of that duplication. If your vertices were A, B, C, D, and E, the diagonal from C to A is the same diagonal you drew from A to C. You can draw two diagonals from that vertex, and there are five vertices, so there are 10 diagonals in a pentagon, right? So you have five places to start, but you can’t end where you started, and you can’t trace over a side, so you have only two places to end. If you try to draw to the other two, you’ll be tracing over a side. Of those four, you can only draw diagonals to two others. You can start a diagonal from any one of the five vertices, but once you pick the starting point, you have four vertices left. Let’s start with a pentagon, with five sides and five vertices. How many are there in a pentagon? Or a hexagon? A triangle with three vertices has no diagonals, but a quadrilateral with four vertices has two diagonals. The more sides a polygon has, the more vertices it has, so the more diagonals you can draw. A polygon with seventeen sides would be a seventeen-gon. When there isn’t a particular name for a polygon with that number of sides, you just tack -gon on to the number of sides. Remember that the name of a polygon is determined by how many sides it has.

Even those rules will depend on the number of sides, but once you know that, you can figure out some things. The other polygons have more sides, more vertices, more angles, and more diagonals, and there are a few rules they all follow. Quadrilaterals and Other PolygonsĪlthough triangles and quadrilaterals are the polygons you meet most often and the ones about which you have the most information, there are others.

Four sided shape called