Definition and designation of perpendicular lines

 

Two intersecting lines are called perpendicular if they form four right angles (i.e. the measure of each angle is equal to 90°). The perpendicularity of lines is designated by the following sign: ⊥

For example, if line a is perpendicular to line b, it can be written as follows:

Definition of perpendicular lines

Definition of perpendicular lines

a and b are perpendicular lines

An example of perpendicular lines

 

Consider two intersecting lines AB and CD.

They form four non-straight angles: СОА, АОD, DOB and ВОС.

Consider angles СОА and АОD.

They are adjacent angles as AO is the common side and OC is a continuation of side DO.

The sum of adjacent angles is 180°.

If ∠СОА = 90° (right angle), then:

An example of perpendicular lines

Consider angles ∠АОС and ∠СОВ. They are adjacent angles. Therefore, if  ∠АОС = 90°, then:

An example of perpendicular lines

As lines AB and CD form four right angles, then these lines are perpendicular:

An example of perpendicular lines

AB and CD are perpendicular lines

AB and CD are perpendicular lines