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related to: corresponding angles in a parallelogram
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Rectangle – A parallelogram with four angles of equal size (right angles). Rhombus – A parallelogram with four sides of equal length. Any parallelogram that is neither a rectangle nor a rhombus was traditionally called a rhomboid but this term is not used in modern mathematics. [1] Square – A parallelogram with four sides of equal length ...
The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.
The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.
Rhomboid: a parallelogram in which adjacent sides are of unequal lengths, and some angles are oblique (equiv., having no right angles). Informally: "a pushed-over oblong". Not all references agree; some define a rhomboid as a parallelogram that is not a rhombus. [4] Rectangle: all four angles are right angles (equiangular). An equivalent ...
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 sum of the squares of the diagonals (the parallelogram law).
Corresponding angles are the four pairs of angles that: have distinct vertex points, lie on the same side of the transversal and; one angle is interior and the other is exterior. Two lines are parallel if and only if the two angles of any pair of corresponding angles of any transversal are congruent (equal in measure).
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Such angles are called a linear pair of angles. [20] However, supplementary angles do not have to be on the same line and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.