Intersecting, Parallel, Perpendicular Lines

Background

We've talked about the drawing of a line. So what happens if we have a second line interact with that first one?

Question

Draw a line and a point not part of that line, labeled Point A. If we draw a line through Point A, in how many ways can the two lines interact? 

Answer

Two ways - they can not intersect (i.e. be parallel) or they can intersect. If they do intersect, there is one way they can form equal angles (i.e. be perpendicular).

Analysis

Let's draw the asked for elements. Point A will be in red:



If we draw lines through the red point, there are an infinite number of lines that will intersect the green line (either on the screen shot, or further off):



Of all the lines that can pass through the red point, only one will never intersect the green line:



This one red line that will never intersect the green line, we can say that the two lines are parallel.

Let's look again at a red line that intersects the green line:



Let's look at the blue arc and the black arc - they are two different lengths. There is only one intersection between the red and green lines where the two arcs are the same length:



The red and green lines are said to be perpendicular.

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Geometry:

• Points, Line Segment, Line

Where might we go?

Graphing:

• X, Y Axes 

Geometry:

• Defining a Circle and Right Angles
• Perimeter and Area