Perpendicular lines

By Alma Villarreal

What are perpendicular lines?

Perpendicular lines are

lines, segments, or rays

that intersect to form right

angles.

Perpendicular to

Parallel

Perpendicular rotate one line 90° parallel

Question: What is the difference between perpendicular and parallel? Answer: 90 degrees (a right angle).If you rotate a perpendicular line by 90° it will become parallel (but not if it touches), and the other way around.

How to know if lines are perpendicular.

•

A line meeting another at a

right angle or 90° is said to be

perpendicular to it. Two lines

are perpendicular if the product

of their slopes is -1. Also, the

two intersecting lines form right

angles.

Perpendicular Lines in Algebra

If two nonvertical lines are perpendicular, then their slopes are negative reciprocals (opposite reciprocals) of one another, or the product of their slopes is –1.

Perpendicular Lines in Algebra

Conversely, if the slopes of two lines are opposite reciprocals of one another, or the product of their slopes is –1, then the lines are nonvertical perpendicular lines.

How Perpendicular Lines May Look

Perpendicular lines may also look like this. These lines are still perpendicular because all the angles are 90.

Perpendicular Lines

Lines do not have to intersect to be perpendicular. In the figure below, the two lines are perpendicular to each other even though they do not touch.

Perpendicular Lines

You can test if lines are perpendicular by extending the lines until they cross. If they do not cross, then they are parallel.

How to Draw Perpendicular Lines Steps 1 & 2

Step1: Start with a line and point K on that line.Step2: Set the compass width to a medium setting. The actual width does not matter..

Step 3

Step 3: Without changing the compass width, mark a short arc on the line at each side of the point K, forming the points P, Q. These two points are the same distance from K.

Steps 4 & 5

Step4: Mark off an arc on one side of the line.Step5: With the compass on P, set its width to any setting beyond K.

Step6: Without changing the compass width, repeat from point Q so that the two arcs cross each other, creating the point R.Step7: Using the straight edge, draw a line from K to where the arcs cross.Step8: Done. The line KR just drawn is perpendicular to the line PQ at K.

Steps 6, 7 & 8