Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects.

A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.

Perpendicularity easily extends to segments and rays. For example, a line segment ${\displaystyle {\overline {AB}}}$ is perpendicular to a line segment ${\displaystyle {\overline {CD}}}$ if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols, ${\displaystyle {\overline {AB}}\perp {\overline {CD}}}$ means line segment AB is perpendicular to line segment CD.

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