In this lesson, we'll discuss some fundamental objects in geometry. The objects we'll discuss are some of the building blocks we use to describe all geometrical objects.
A point is an exact location in space. It has no size (i.e., no length, width, or depth), only position. A point is indicated with a dot usually labeled with a capital letter (e.g., , , , ...), as shown below.
A line is a straight object that is infinitely long and has no width. We can think of it as an infinite collection of points, extending infinitely in both directions. A line has no endpoints!
Let's take a look at the following line.
A line that passes through the points and is expressed as
We use the "" symbol to denote that the line extends forever in both directions.
Lines can also be indicated with lowercase letters. For example:
What is the correct way to represent the line shown below?
Since the line passes through the points and we can represent this line as follows:
We use the "" symbol to denote that the line extends forever in both directions.
Which of the following diagrams shows a line?
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a
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b
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c
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d
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e
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What is the correct way to represent the line shown above?
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a
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$\overset{\longrightarrow}{PQ}$ |
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b
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$\overline{PQ}$ |
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c
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$\overset{\longleftarrow}{PQ}$ |
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d
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$\overset{\longleftrightarrow}{PQ}$ |
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e
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$PQ$ |
A ray is similar to a line but has a starting point and extends infinitely in one direction only. An example of a ray is shown below.
A ray that starts at the point and passes through a point is expressed as
We use the "" symbol to denote that the line extends forever in one direction. Notice that the arrow's tail is above the starting point
Similar to lines, rays have no width but are infinite in length.
Consider the points and shown above. Draw the ray
Note the following:
A ray is a straight object with a specific starting point and extends forever in one direction.
Using diagrams, a ray is shown with an arrow on one side.
In our case, the starting point is and the ray extends in the direction. Therefore, we can draw the ray as follows:
Which of the following diagrams shows a ray?
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a
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b
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c
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d
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e
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What is the correct way to represent the ray shown above?
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a
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$\overset{\longrightarrow}{QP}$ |
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b
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$\overline{PQ}$ |
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c
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$PQ$ |
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d
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$\overset{\longrightarrow}{PQ}$ |
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e
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$\overset{\longleftrightarrow}{PQ}$ |
A segment is part of a line bounded by two points, called the endpoints of the segment. An example of a segment is shown below.
A segment with endpoints and is denoted
What is the correct way to represent the line segment shown above?
Since the segment has endpoints and we can represent this line segment as follows:
We draw a horizontal line with no arrows above our letters to denote that the line does not extend forever.
Which of the following diagrams shows a line segment?
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a
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b
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c
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d
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e
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What is the correct way to represent the line segment shown above?
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a
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$\overset{\longrightarrow}{SP}$ |
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b
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$\overset{\longrightarrow}{PS}$ |
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c
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$\overset{\longleftrightarrow}{PS}$ |
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d
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$\overline{PS}$ |
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e
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$PS$ |