When 2 lines intersect at a appropriate angle, they room perpendicular lines. Us can additionally say the if 2 lines are perpendicular, then your intersection forms a ideal angle. Periodically in everyday language, components of present (rays and also line segments) that fulfill at right angles are likewise called perpendicular lines.

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Lines l and m are perpendicular due to the fact that they meet at a ideal angle. We have the right to write l⊥m to show this, whereby "⊥" is the symbol because that perpendicular.

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


Properties that perpendicular lines

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


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

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


The steep of line ns is ½ and the slope of line r is -2, the an unfavorable reciprocal of ½, for this reason p and also q room perpendicular and also meet at a best angle.

Knowing that 2 perpendicular lines accomplish at a appropriate angle, or that if your intersection creates a appropriate angle that they room perpendicular, is advantageous information in working with postulates, theorems, and other properties in Geometry. Listed below are a couple of examples.

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


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

• If a transversal is perpendicular to among a pair that parallel lines (or number of parallel lines), it must be perpendicular to every the parallel lines.


In the chart above, m//n and l⊥m. Due to the fact that l⊥m, all four angles created by the intersection of l and also m are best angles. Also, since m//n all four angles are likewise right angles created by lines l and n, by the residential or commercial property of matching angles that parallel lines gift congruent. Thus, line l is also perpendicular to heat n.

Did you know?

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

See more: List All The Factors Of 56, Factors Of 56 In Pairs (Factor Pairs For 56)


Also, every horizontal grid line is perpendicular to every vertical grid line the comprises the grid for the system. The Cartesian coordinate mechanism is also known as an orthogonal (meaning at ideal angles) coordinate system.