When 2 lines intersect at a ideal angle, they room perpendicular lines. Us can likewise say that if 2 lines are perpendicular, then their intersection develops a best angle. Sometimes in day-to-day language, components of present (rays and line segments) that accomplish at ideal angles are also called perpendicular lines.

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Lines l and also m room perpendicular since they satisfy at a ideal angle. We have the right to write l⊥m to present this, where "⊥" is the symbol for perpendicular.

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


Properties of perpendicular lines

• There deserve to be just one line the is perpendicular to a offered line at a offered point.


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

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


The slope of line p is ½ and also the steep of line r is -2, the negative reciprocal of ½, so p and q are perpendicular and also meet in ~ a appropriate angle.

Knowing that 2 perpendicular lines satisfy at a ideal angle, or the if your intersection forms a right angle the they room perpendicular, is useful information in working with postulates, theorems, and other properties in Geometry. Below are a few examples.

• If the 2 non-adjacent political parties of 2 acute nearby angles room perpendicular then, the angles have to be complementary.


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

• If a transversal is perpendicular to among a pair the parallel lines (or several parallel lines), it must be perpendicular to all the parallel lines.


In the chart above, m//n and also l⊥m. Due to the fact that l⊥m, all four angles developed by the intersection the l and m are appropriate angles. Also, since m//n all 4 angles are also right angles created by lines l and n, through the property of equivalent angles of parallel lines gift congruent. Thus, heat l is additionally perpendicular to line n.

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

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Also, every horizontal grid line is perpendicular to every vertical net line that comprises the grid for the system. The Cartesian coordinate device is additionally known as an orthogonal (meaning at appropriate angles) name: coordinates system.