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Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...
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 ...
A rhombus with a right vertex angle; A rhombus with all angles equal; A parallelogram with one right vertex angle and two adjacent equal sides; A quadrilateral with four equal sides and four right angles; A quadrilateral where the diagonals are equal, and are the perpendicular bisectors of each other (i.e., a rhombus with equal diagonals)
Furthermore, let E and F the midpoints of its diagonals AC and BD and P be the center of its incircle. Given such a configuration the point P is located on the Newton line, that is line EF connecting the midpoints of the diagonals. [1] A tangential quadrilateral with two pairs of parallel sides is a rhombus.
The parallelogram between the pair of upright grey triangles has perpendicular diagonals in ratio , hence is a golden rhombus. If the triangle has legs of lengths 1 and 2 then each discrete spiral has length φ 2 = ∑ n = 0 ∞ φ − n . {\displaystyle \varphi ^{2}=\sum _{n=0}^{\infty }\varphi ^{-n}.}
The golden rhombus. In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: [1] = = + Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle. [1]
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