How to Recognize Parallel and Perpendicular Lines

Two lines are parallel if they have the same slope. Two lines are perpendicular if their slopes are negative reciprocals of one another. Numbers that are negative reciprocals have a product –1.

Consider the following slopes of some lines or line segments:

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Here are the slopes of the lines that are parallel:

  • m1 = 1/2 and m4 = 5/10 have the same slope.

  • m2 = –2 and m5 = –14/7 also have the same slope.

Here are the slopes of the lines that are perpendicular:

  • m1 = 1/2 and m2 = –2 have slopes that are negative reciprocals.

  • m4 = 5/10 and m5 = –14/7 also have slopes whose product is –1.

As a matter of fact, because the lines with slopes of 1/2 and 5/10 are equal to one another, they're both perpendicular to the lines with slopes of –2 and –14/7, which are also equal in slope. It's one big, happy family.

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