example of a straight line
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What is a Straight Line?
By definition, a straight line is the set of all points between and extending beyond two points. In most geometries, a line is a primitive object that does not have formal properties beyond length, its single dimension.
The two properties of straight lines in Euclidean geometry are that they have only one dimension, length, and they extend in two directions forever.
Properties of Straight Lines
One-dimensional
Can be horizonal, vertical, or diagonal
Both ends extend in two directions forever
Makes a 180-degree angle when drawing an angle arc from one point to another
What is a Point?
A point is the simplest figure in geometry. It is a location in space, without dimension. It has no width, volume, thickness, length or depth. Yet when you have two points, if you connect every point between those two points, you have a straight line.
Points on a line are collinear (col = "with," or "together" and linear = "string," or "line"). Only two points are needed to determine a line.
Naming & Identifying Straight Lines
Straight lines are named by any two points on their length. Generally you name them from left to right. Here is line AB:
[insert drawing of line AB]
To identify a line in writing, you write the two points as capital letters and draw a tiny two-headed line above the two letters, like this:
[plug in the graphic of the symbol]
How To Construct a Straight Line
A straight line is one of the easiest constructions to make in geometry. With a sheet of blank paper, a pencil, and a straightedge, you can construct a line easily:
Draw two dots on the paper, some distance from each other; these are Points
Use the straightedge to connect the two Points with a pencil line, and extend the line far past both Points
Draw arrowheads at the ends of the line you drew
Line Segments and Rays
Straight lines are considered infinite in two directions, along their length. Because of this, you seldom use pure lines in everyday geometry. You take snippets of straight lines:
Line segment -- A line segment is a segment, or finite portion, of an infinite straight line
Ray -- A ray is an infinite portion of a straight line; it has a single point of origin but continues in one direction forever
Here is line segment CD:
[insert drawing of line segment CD]
And here is ray EF:
[insert drawing of ray EF]
Line segments are used to construct sides of all polygons. Rays are used to make angles. Line segments and rays are both portions or segments of straight lines.
What About Curves?
A curve is not a straight line, just as a straight line is not a curve. A curved line contains points that are not linear to two given points. The curve moves in other directions from the straight line created by joining collinear points.
Direction of Straight Lines
Straight lines can be horizontal, which is to say moving left and right of your viewing spot, forever. Straight lines can be vertical, which is to say rising above and plunging below your viewing spot, forever. Straight lines can be diagonal, which means they are any angle other than horizontal or vertical.
Straight lines can be alone or in pairs. Pairs of straight lines can run parallel to one another, never getting closer or further apart. They are identified with the symbol ∥.
Pairs of straight lines can also intersect each other at any angle. When two straight lines intersect at 90°, they are perpendicular, identified with the symbol ⊥.
Straight Angles
Straight lines can appear to be another figure, and vice versa. A straight angle, 180°, is a straight line. A straight angle is constructed of two rays with a common endpoint. Since the two rays share a common endpoint and each ray continues in one direction forever, the only "giveaway" that you have a straight angle (and not a straight line) may be the three identified points (instead of two) along the figure:
[insert drawing of straight angle with three labeled points left, center, right]
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illustration 1: reduce 3x-4y+5=0 to all other forms...