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A square is a rhombus with all angles equal. [1] A square is a parallelogram with one right angle and two adjacent equal sides. [1] A square is a quadrilateral with four equal sides and four right angles; that is, it is a quadrilateral that is both a rhombus and a rectangle [1]
The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square. [ 8 ] If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area.
The ratio between the areas of similar figures is equal to the square of the ratio of corresponding lengths of those figures (for example, when the side of a square or the radius of a circle is multiplied by three, its area is multiplied by nine — i.e. by three squared). The altitudes of similar triangles are in the same ratio as ...
For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomboid, a specific subtype of parallelogram); however, while all rhomboids ...
The first property implies that every rhombus is a parallelogram. A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the ...
This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid. This is also advocated in the taxonomy of quadrilaterals. Under the inclusive definition, all parallelograms (including rhombuses, squares and non-square rectangles) are trapezoids. Rectangles have mirror symmetry on mid-edges; rhombuses ...
Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [1] but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. [2] [3] A kite may also be called a dart, [4] particularly if it is ...
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