Search results
Results From The WOW.Com Content Network
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.
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.
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .
The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length. The figure formed by joining the midpoints of the sides of a rhombus is a rectangle, and vice versa.
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.
In any quadrilateral, the four edge midpoints form a parallelogram, the Varignon parallelogram, whose sides are parallel to the diagonals and half their length.It follows that, in an equidiagonal and orthodiagonal quadrilateral, the sides of the Varignon parallelogram are equal-length and perpendicular; that is, it is a square.
Therefore, the pole of each diagonal is contained in the other diagonal respectively. [2] [3] Angles ∠BMC and ∠DMC are equal. The bisectors of the angles at B and D intersect on the diagonal AC. A diagonal BD of the quadrilateral is a symmedian of the angles at B and D in the triangles ∆ ABC and ∆ ADC.
According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.