Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a pair of angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
s is said to be vertical (also opposite and vertically opposite, which is abbreviated as vert. opp. ∠s) if the angles are formed from two intersecting lines
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
and the angles are not adjacent. The two angles share a vertex. Such angles are equal in measure and can be described as "equal" (in the UK or the USA) or "congruent
In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...
" (in the USA).
When two straight lines intersect at a point, four angles are made.