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Parallel and Perpendicular Lines

Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane).
Parallel Lines in greater depth

On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of  these lines intersects at 90 degrees.
Perpendicular Lines in greater depth.
Parallel & Perpendicular Lines Applet
applet
Parallel Lines Lines worksheet
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Perpendicular Lines worksheet
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Example of parallel lines.


As you can see from the diagram below, these lines
  • have the same slope
    • 2
  • are never going to intersect

Example of perpendicular lines.


As you can see from the picture below:
Diagram of two parallel lines with equal slope


Applet

See Applet on its own page
Click and drag the points below to explore the relationship between parallel lines, perpendicular lines, slope and the graph of a line.
Slope Interept Form
Point Slope Form
Slope?
Draw Rise and Run ?
Show Rise and Run Text?
Line Types [Parallel/Perpendicular/ Both]
$$ $$
$$ $$ $$ $$





 Parallel lines in greater depth 

Both of the lines below have the same slope: $$ \frac{1}{2} $$
Therefore these lines are parallel and will never meet. Example of two parallel lines
Are the two lines pictured below parallel?

Answer
No

While these lines may look parallel at first glance, if you look closely and calculate each line's slope, you will find that:
    line 1 has a slope of $$ -\frac{1}{4} $$
    line 2 's slope is  $$ - \frac{1}{3} $$.
Classify these lines as parallel or not
Are the two lines below parallel?
Answer
Yes these lines have the same slope, 2, and clearly are never going to intersect.
Parall Lines Image

 

Are the two lines in the picture below perpendicular?

Answer

Yes.
The slope of line 1 is -2 and
that of line 2 is $$ \frac{1}{2}$$.
-2 and$$ \frac{1}{2}$$  are negative reciprocals so the liens are perpendicular..

Determine whether or not lines 6 and 5 perpendicular?


Answer
Yes.
Line 5 's slope is $$ \frac{3}{2}$$ and line 6 's is$$ -\frac{2}{3}$$ , which are negative reciprocals.
Are Line P and line L perpendicular?

Answer

They are not perpendicular because their slopes are not negative reciprocals of one another.


Example of Perpendicular Lines
Parallel & Perpendicular Lines Applet
applet
Parallel Lines Lines worksheet
worksheet icon
Perpendicular Lines worksheet
worksheet icon