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In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics , where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.
a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram) a quadrilateral with four sides of equal length (by definition) a quadrilateral in which the diagonals are perpendicular and bisect each other; a quadrilateral in which each diagonal bisects two opposite interior angles
Orthodiagonal quadrilateral: the diagonals cross at right angles. Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects the other into equal lengths. Every dart and kite is bisect-diagonal. When both diagonals bisect another, it's a parallelogram.
In elementary geometry, a quadrilateral whose diagonals are perpendicular and of equal length has been called a midsquare quadrilateral (referring to the square formed by its four edge midpoints). [ 1 ] [ 2 ] These shapes are, by definition, simultaneously equidiagonal quadrilaterals and orthodiagonal quadrilaterals . [ 2 ]
Every kite is an orthodiagonal quadrilateral, meaning that its two diagonals are at right angles to each other. Moreover, one of the two diagonals (the symmetry axis) is the perpendicular bisector of the other, and is also the angle bisector of the two angles it meets. [1] Because of its symmetry, the other two angles of the kite must be equal.
The central angle of a square is equal to 90° (360°/4). The external angle of a square is equal to 90°. The diagonals of a square are equal and bisect each other, meeting at 90°. The diagonal of a square bisects its internal angle, forming adjacent angles of 45°. All four sides of a square are equal. Opposite sides of a square are parallel.
The angle between a side and a diagonal is equal to the angle between the opposite side and the same diagonal. The diagonals cut each other in mutually the same ratio (this ratio is the same as that between the lengths of the parallel sides). The diagonals cut the quadrilateral into four triangles of which one opposite pair have equal areas ...
Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent ...