What is the relationship between two perpendicular lines? What are some examples?

Question

Violet Aldrich · Accepted Answer

All four angles formed by two perpendicular lines are measured #90^o#.

By definition, perpendicular lines are those that intersect at right angle.

The definition requires only one angle (out of four formed by two intersecting lines) to be the right angle (that is, measure at #90^o#). Obviously, all others are also measure #90^o# since an angle adjacent to one measured #90^o# must complement it to a straight angle of #180^o# and, hence, must be #90^o# itself.

Example of perpendicular lines:

Violet Aldrich · Answer

undefined Two perpendicular lines intersect at a right angle, forming four right angles where they meet. Perpendicular lines have slopes that are negative reciprocals of each other. For example, if one line has a slope of m, then the slope of the perpendicular line would be -1/m.

Examples of perpendicular lines include:

1. The x-axis and the y-axis in a Cartesian coordinate system.
2. The sides of a square, rectangle, or any other regular polygon where adjacent sides meet at right angles.
3. The diagonals of a rectangle, which intersect at right angles.
4. The edges of a cube or rectangular prism.
5. The altitude and base of a right triangle drawn from one vertex to the opposite side, where the altitude is perpendicular to the base.