A diagonal is a line segment that connects two nonadjacent vertices of a polygon. In a quadrilateral, such as a square or rectangle, there are two diagonals that connect opposite corners. These diagonals create four right triangles within the quadrilateral. The length of a diagonal can be found using the Pythagorean theorem, by squaring the lengths of the two sides that the diagonal connects, summing them, and then taking the square root of the sum.
In a three-dimensional space, diagonals can also refer to line segments that connect two nonadjacent vertices of a solid shape, such as a cube or rectangular prism. These diagonals can help determine the length of the space diagonal, which is a line segment that connects two opposite corners of a three-dimensional figure.
Overall, diagonals play a crucial role in geometry by connecting vertices, creating triangles, and helping to calculate lengths within polygons and solid shapes.
Image by V A N D E E from Flickr.
