Perpendicular Lines: Properties, Angles, And Uses In Geometric Figures

perpendicular lines

Two lines that intersect to form right angles

Perpendicular lines are two lines that intersect at a right angle (90 degrees). The word perpendicular comes from the Latin perpendiculum, which means plumb line. There are a few key properties of perpendicular lines:

1. They have opposite reciprocal slopes. That means if one line has a slope of m, the other line must have a slope of -1/m. For example, if one line has a slope of 2/3, the other line must have a slope of -3/2.

2. The product of their slopes is -1. This is another way of expressing the first property; if two lines are perpendicular, then their slopes must multiply to -1.

3. The angles formed by two perpendicular lines are always congruent, or equal in measure. This means that each of the four angles formed by a pair of perpendicular lines is 90 degrees.

4. Perpendicular lines can be found in many geometric figures, such as squares and rectangles, where the sides are all perpendicular to each other.

To determine if two lines are perpendicular, you can check their slopes. If the slopes are opposite reciprocals of each other, then the lines are perpendicular. For example, if one line has a slope of 2/3, the perpendicular line will have a slope of -3/2.

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