When 2 lines crossing at a ideal angle, they space perpendicular lines. We can likewise say the if 2 lines room perpendicular, then your intersection forms a right angle. Sometimes in daily language, components of lines (rays and line segments) that fulfill at ideal angles are also called perpendicular lines.

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Lines l and m space perpendicular because they fulfill at a best angle. We have the right to write l⊥m to show this, whereby "⊥" is the symbol for perpendicular.

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


Properties of perpendicular lines

• There can be just one line that is perpendicular come a provided line at a provided point.


Let currently m, n, and also l intersect at suggest P above. If the angle developed by l and m is a right angle, then the angle developed by lines l and also n cannot likewise be a ideal angle.

• 2 lines space perpendicular if their slopes are an unfavorable (or opposite) reciprocals of every other.


The slope of line p is ½ and also the steep of heat r is -2, the an unfavorable reciprocal of ½, so p and q space perpendicular and meet in ~ a ideal angle.

Knowing that two perpendicular lines accomplish at a appropriate angle, or that if their intersection forms a best angle that they room perpendicular, is advantageous information in working v postulates, theorems, and also other properties in Geometry. Below are a few examples.

• If the 2 non-adjacent sides of two acute surrounding angles are perpendicular then, the angles must be complementary.


∠BAD and also ∠CAD are nearby angles, through non-adjacent, perpendicular sides abdominal muscle and AC. Since abdominal and AC are perpendicular, ∠BAC is a right angle measure up 90° so, ∠BAD + ∠CAD = 90°.

• If a transversal is perpendicular to among a pair the parallel present (or number of parallel lines), it need to be perpendicular to all the parallel lines.


In the chart above, m//n and l⊥m. Since l⊥m, all four angles developed by the intersection the l and m are appropriate angles. Also, due to the fact that m//n all four angles are additionally right angles formed by lines l and also n, by the building of corresponding angles that parallel lines being congruent. Thus, line l is also perpendicular to line n.

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The x- and y-axis space two present in the Cartesian coordinate aircraft that space perpendicular to every other.

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Also, each horizontal grid heat is perpendicular to each vertical net line that comprises the grid because that the system. The Cartesian coordinate system is additionally known as an orthogonal (meaning at right angles) name: coordinates system.