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In geometry, the segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
A vector quantity is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a directed line segment. A vector is frequently depicted graphically as an arrow connecting an initial point A with a terminal point B , [ 3 ] and denoted by A B . {\textstyle {\stackrel {\longrightarrow }{AB}}.}
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry.It is the length of the line segment which joins the point to the line and is perpendicular to the line.
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Illustration of angle addition formulae for the sine and cosine of acute angles. Emphasized segment is of unit length. Diagram showing the angle difference identities for sin ( α − β ) {\displaystyle \sin(\alpha -\beta )} and cos ( α − β ) {\displaystyle \cos(\alpha -\beta )}