Right angle
Elementary
A right angle is an angle that is a quarter of a full turn, like the corner of a square or of a sheet of paper.
High school
A right angle is an angle that measures
\[90^\circ = \frac{\pi}{2} \text{ radians}.\]Examples
Examples
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Two adjacent sides of a rectangle, as segments meeting at a corner
Elementary
The angle at the corner of a rectangle where two adjacent sides meet is a right angle, because every angle of a rectangle measures $90^\circ$.
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The lines $y = x$ and $y = -x$ in the plane, with direction vectors $(1, 1)$ and $(1, -1)$
High school
The lines $y = x$ and $y = -x$ cross at the origin and form four right angles there.
Non-examples
Things that may be mistaken for examples.
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The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis in $\reals^3$
High school
The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis do not form a right angle, because the lines have no common point at which to form an angle.
Properties
- A right angle is formed by two rays or segments that share an endpoint; the term describes the angle, not the lines.
Distinctions involving this term
- Right angle vs. perpendicular vs. orthogonal vs. normal: Right angles, perpendicular lines, orthogonal vectors, and normal vectors all describe things that meet “squarely.” A right angle is an angle of $90^\circ$, so the term describes an angle. Perpendicular describes lines or planes that intersect and form right angles. Orthogonal describes vectors whose inner product is $0$, which extends the idea to vectors that do not meet, such as directions of skew lines, to the zero vector, and to vectors that are not arrows, such as functions. A normal vector is perpendicular to a line, curve, or surface at a point, so the term describes a vector relative to a shape.