# Perpendicular lines

When 2 lines intersect at a right angle, they are perpendicular lines. We can also say that if 2 lines are perpendicular, then their intersection forms a right angle. Sometimes in everyday language, parts of lines (rays and line segments) that meet at right angles are also called perpendicular lines.

Lines l and m are perpendicular because they meet at a right angle. We can write l⊥m to show this, where "⊥" is the symbol for perpendicular.

Also, if two lines are perpendicular, 4 right angles are created. In the diagram below, angles 1, 2, 3, 4 are all right angles.

## Properties of perpendicular lines

• There can be only one line that is perpendicular to a given line at a given point.

Let lines m, n, and l intersect at point P above. If the angle formed by l and m is a right angle, then the angle formed by lines l and n cannot also be a right angle.

• Two lines are perpendicular if their slopes are negative (or opposite) reciprocals of each other.

The slope of line p is ½ and the slope of line r is -2, the negative reciprocal of ½, so p and q are perpendicular and meet at a right angle.

Knowing that two perpendicular lines meet at a right angle, or that if their intersection forms a right angle that they are perpendicular, is useful information in working with postulates, theorems, and other properties in Geometry. Below are a few examples.

• If the two non-adjacent sides of two acute adjacent angles are perpendicular then, the angles must be complementary.