Polygons and Diagonals

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 1 of 61.

A polygon is a closed shape made of straight sides. Each side meets the next one at a corner, a vertex. Polygons are named by how many sides they have: a triangle has 3, a quadrilateral 4, a pentagon 5, a hexagon 6 and an octagon 8. To name one, read its vertices in order round the edge: pentagon ABCDE.

$Hexagon ABCDEF with the three diagonals from A drawn$

A diagonal joins two vertices that are not next to each other. In hexagon ABCDEF, AB and AF are sides, because B and F are the neighbours of A. AC, AD and AE are the diagonals from A. A vertex has no diagonal to itself or to its two neighbours, so a hexagon has 6 − 3 = 3 diagonals from each vertex.

Those diagonals from one vertex cut the hexagon into four triangles. That is how you will find the angles of any polygon in the next lessons.