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A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. [13] ... The height (or altitude) is the perpendicular distance between the bases.
A right trapezoid is a trapezoid that has two pairs of adjacent sides that are perpendicular. Each of the four maltitudes of a quadrilateral is a perpendicular to a side through the midpoint of the opposite side.
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
Brahmagupta's theorem states that for a cyclic orthodiagonal quadrilateral, the perpendicular from any side through the point of intersection of the diagonals bisects the opposite side. [ 3 ] If an orthodiagonal quadrilateral is also cyclic, the distance from the circumcenter (the center of the circumscribed circle) to any side equals half the ...
An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular. [ 3 ] A convex quadrilateral with diagonal lengths p {\displaystyle p} and q {\displaystyle q} and bimedian lengths m {\displaystyle m} and n {\displaystyle n} is equidiagonal if and only if [ 4 ] : Prop.1
By applying the Pythagorean theorem to the right triangle AWP, and observing that WP = AZ, it follows that A P 2 = A W 2 + W P 2 = A W 2 + A Z 2 {\displaystyle AP^{2}=AW^{2}+WP^{2}=AW^{2}+AZ^{2}} and by a similar argument the squares of the lengths of the distances from P to the other three corners can be calculated as
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Since and are both perpendicular to , they are parallel and so the quadrilateral is a trapezoid. The theorem is proved by computing the area of this trapezoid in two different ways. The theorem is proved by computing the area of this trapezoid in two different ways.