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.