Notes
Definition
Diagonal- a line segment connecting two nonadjacent vertices
Number of Diagonals in a Polygon (n-gon)
\( \text{Diagonals} = \frac{n(n-3)}{2}\)
| \({\text{Number of diagonals in polygons}}\) | ||
| Triangle (3 sides) | No diagonals |  |
| Quadrilateral (4 sides) | 2 diagonals |  |
| Pentagon (5 sides) | 5 diagonals |  |
| Hexagon (6 sides) | 9 diagonals |  |
| Octagon (8 sides) | 20 diagonals |  |
| N-gon (n sides) | \(\frac{n(n-3)}{2}\) diagonals | |
| \({\text{Properties of Diagonals of Quadrilaterals}}\) | |
| Parallelograms | Diagonals bisect each other |
| Rectangles | Diagonals bisect each other Diagonals are congruent |
| Rhombuses | Diagonals bisect each other Diagonals are perpendicular |
| Squares | Diagonals bisect each other Diagonals are perpendicular Diagonals are congruent |
| Kites | Diagonals are perpendicular to each other |
| Isosceles Trapezoids | Diagonals are Congruent |
See Related Pages\(\)
\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Intro to Polygons}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Area of a Regular Polygon (Apothem)}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Population Density}\)
\(\,\,\,\,\,\,\,\,\)
In Summary
Diagonals of polygons are line segments that connect two non-adjacent vertices of a polygon. They are different from the sides of the polygon, which are the line segments that connect adjacent vertices.
We learn about diagonals of polygons in math classes because they are an important concept in geometry. Understanding diagonals can help us better understand the properties and characteristics of different types of polygons, such as triangles, quadrilaterals, and pentagons.
A fun fact about diagonals of polygons is that the number of diagonals in a polygon can be calculated using a simple formula. The number of diagonals in a polygon with n vertices is given by the equation: \(\displaystyle\frac{n(n-3)}{2}\).
Some related topics to diagonals of polygons include other concepts in geometry, such as angles, triangles, and quadrilaterals. Understanding diagonals can also help us better understand more advanced concepts in geometry, such as tessellations and non-Euclidean geometry.