A diagonal line of a polygon is a line that joins any two vertices not already joined by a side.
A polygon with n sides has n(n-3)/2 diagonals
→ a quadrilateral with 4 sides has 4(4-3)/2 = 4 × 1 ÷ 2 = 2 diagonal
Quadrilaterals include:
Squares, rectangles, rhombuses, parallelograms, kites, trapezia (trapezoids).
The diagonals of a quadrilateral divide the quadrilateral into 4 triangles. depending upon the quadrilateral some, or all of the triangles may be congruent.
The properties of the diagonals of each quadrilateral are:
- square: equal and bisect each other at 90°; the triangles formed are all congruent
- rectangle: equal and bisect each other but not at 90°; the triangles formed are all congruent
- rhombus: not equal but bisect each other at 90°; the triangles formed are all congruent
- parallelogram: not equal but do bisect each other, but not at 90°; the triangles formed are congruent in (opposite) pairs
- kite: perpendicular and the longer diagonal bisects the shorter diagonal; the triangles formed are congruent in (adjacent) pairs
- trapezium (trapezoid): only of equal length and bisect each other if it is an isosceles trapezium (trapezoid) and the triangles formed are congruent in (opposite) pairs; otherwise they are of differing lengths and just intersect each others and the triangles formed are non-congruent.
