Search results
Results From The WOW.Com Content Network
A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3] 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.
An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...
Furthermore, this point is a tangent point between the side of the reference triangle and its Steiner deltoid. A quadrilateral that is not a parallelogram has one and only one pedal point, called the Simson point, with respect to which the feet on the quadrilateral are collinear. [6]
A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal quadrilaterals that are also equidiagonal quadrilaterals are called midsquare quadrilaterals. [2]
There exists a quadrilateral in which all angles are right angles, that is, a rectangle. There exists a pair of straight lines that are at constant distance from each other. Two lines that are parallel to the same line are also parallel to each other. In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the ...
For a triangle ABC, let l an arbitrary line and A 0 B 0 C 0 the Cevian triangle of an arbitrary point P. l intersects BC, CA, and AB at A 1, B 1, and C 1 respectively. Then AA 1 ∩B 0 C 0, BB 1 ∩C 0 A 0, and CC 1 ∩A 0 B 0 are colinear. If P is the centroid of the triangle ABC, the line is Newton-Gauss line of the quadrilateral composed of ...
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 .
Newton's theorem can easily be derived from Anne's theorem considering that in tangential quadrilaterals the combined lengths of opposite sides are equal (Pitot theorem: a + c = b + d). According to Anne's theorem, showing that the combined areas of opposite triangles PAD and PBC and the combined areas of triangles PAB and PCD are equal is ...