Diagonal
In mathematics, a diagonal refers to a line segment that connects any two non-adjacent vertices of a polygon
In mathematics, a diagonal refers to a line segment that connects any two non-adjacent vertices of a polygon. It can also refer to a segment that connects two opposite corners of a two-dimensional shape, like a square or a rectangle. In other words, a diagonal is the longest distance between two points in a polygon.
For example, in a square, the diagonal is the line segment that connects two opposite corners. It divides the square into two congruent right triangles. The length of a diagonal in a square is equal to the square root of 2 times the length of one side.
In a rectangle, the diagonals are equal in length and bisect each other. The length of a diagonal in a rectangle can be found using the Pythagorean theorem, where the diagonal’s length (d) is the square root of the sum of the squares of the lengths of the rectangle’s sides (a and b): d = √(a² + b²).
The concept of diagonal is not limited to two-dimensional shapes. It can also be applied to three-dimensional figures, such as cubes and rectangular prisms. In a cube, the diagonal is a line segment that connects two opposite corners of the cube. It passes through the center of the cube and divides it into two congruent pyramids.
In summary, a diagonal is a line segment that connects non-adjacent vertices or opposite corners of a polygon or a two-dimensional shape, and it plays an important role in determining the length, symmetry, and geometric properties of various figures.
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