Introduction to Geometry: Basic Elements of Geometry

Lines and Line Segments

A line is a straight collection of an infinite number of points that extends forever in opposite directions.

points A, C and B, in that order, with a line through all three, extending beyond the end points, with arrows on each end

On a sheet of paper, draw one point. How many lines can you draw through the point?

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Now, draw two points. How many lines can you draw through the two points?

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Finally, draw three points that do not lie in a straight line (like the vertices of a triangle). How many lines can you draw that pass through all three of the points?

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As you’ve seen, it takes two distinct points to determine a line.  In order to name the line, we choose any two points on the line and draw a double-sided arrow above the letters to indicate that it extends infinitely in two directions.  The line in the figure could be named A B with a double-sided arrow over it; line A B, line A C, or line C B. The order of the letters in unimportant.  In other words, the line could also be named line B A, line B C or line C A.