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A pair of angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles or vertically opposite angles. They are abbreviated as vert. opp. ∠s. [8]
Alternate angles are the four pairs of angles that: have distinct vertex points, lie on opposite sides of the transversal and; both angles are interior or both angles are exterior. If the two angles of one pair are congruent (equal in measure), then the angles of each of the other pairs are also congruent.
If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264
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. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent ...
A rectilinear polygon has edges of two types: horizontal and vertical. Lemma: The number of horizontal edges is equal to the number of vertical edges (because every horizontal edge is followed by a vertical edge and vice versa). Corollary: Orthogonal polygons have an even number of edges. X marks convex corners; O marks concave corners.
The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles. [6] The vertex opposite the base is called the apex. [7] In the equilateral triangle case, since all sides are equal, any side can be called the base. [8]
Lines and are antiparallel with respect to the line if they make the same angle with in the opposite senses. Two lines l 1 {\displaystyle l_{1}} and l 2 {\displaystyle l_{2}} are antiparallel with respect to the sides of an angle if they make the same angle ∠ A P C {\displaystyle \angle APC} in the opposite senses with the bisector of that angle.
A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular. A parallelogram is a special case of a trapezium (known as a trapezoid in North America) in which both pairs of opposite sides are parallel and equal in length. A trapezium is a convex quadrilateral which has at least one pair of parallel ...