垂直是一个几何术语。在平面几何中，如果一条直线与另一条直线相交，且它们构成的任意相邻两个角相等，那么这两条直线相互垂直。术语“垂直”（符號：⊥）衍生一个形容词（垂直）或者名词（垂线）。因此，根据圖一，直线AB通过B点与直线CD相互垂直。像图一这样，如果一条直线与另一条直线垂直，那么它们构成的两个角称为直角，或者90°角。
垂足指两条互相垂直的线相交的点。
垂直的概念对线段和射线也通用，只需看一者所在的直线是否与另一者所在的直线垂直就可以了。如图一中，线段AB和线段CD相互垂直。甚至线段AB的一端不一定要在线段CD上（即可定向伸缩），它们仍被认为是垂直的。
空间几何中，有直线与直线、直线与平面、平面与平面之间的垂直关系。垂直可以看做是欧几里得空间（或内积空间）中的正交关系在二维和三维空间中的特例。
在笛卡儿坐标系中，两条被如下等式所表示的直线 L {\displaystyle L} 和 M {\displaystyle M}
那么垂直的情况有两种：
如果两条直线的表达式为：
那么只有一种情况：两条直线在这个平面相互垂直当且仅当 a 1 a 2 + b 1 b 2 = 0 {\displaystyle a_{1}a_{2}+b_{1}b_{2}=0}
假如用 V 1 = ( a 1 , b 1 ) {\displaystyle V_{1}=(a_{1},b_{1})} 和 V 2 = ( a 2 , b 2 ) {\displaystyle V_{2}=(a_{2},b_{2})} 来表示两条直线的方向向量，那么上面垂直的充分必要条件就是两个方向向量正交的充分必要条件。这说明了垂直实际上是正交关系（在二维和三维空间）的一个特例。
三维空间中不仅有直线与直线的垂直，也有直线与平面、平面与平面的垂直。
用尺规作一条过点P与直线AB相互垂直的直线，过程如下（见圖二）：
为证明直线PQ与直线AB垂直，使用三角形SSS全等定理证明三角形QPA'和QPB'全等以求得三角形OPA'和OPB'也全等。然后使用三角形SAS全等定理证明角POA和POB相等。
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