Points, Lines, Segments, Angles etc.

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K-12: Materials at high school level.



Points and Lines

A point is a specific location in space. A point is drawn as a dot. Often we label a point with some letter. We would say "Point A" for instance.

Dot.png

Above you see three points labeled A, B and C.

Lines are something you have seen in Algebra. Straight lines go on infinitely far in both directions. Closely related to the line are rays and line segments.

A ray is what we can think of as "half a line". A ray starts at a given point and then goes of to infinity in one direction.

A line segment is just a small part of a line. It starts at one point and ends at another.

Line-ray-segment.png

In the picture above we see the difference between a line, a ray and a segment. The line is the figure at the top. There are no points at the end, and we are supposed to think of the line as going off to infinity at both ends. The figure in the middle is a ray. It starts at point A and then moves off to the right. The line segment is all the way at the bottom.

Example showing several line segments and their labels

We will be using line segments a lot in later sections. We will label segments by recording the endpoints. For example:

Triangle-segments.png

In this diagram we see several line segments:

  • Segment AP is the line segment connecting A and P. Note that we can also call this segment PA.
  • Segment AB (or BA if you like) runs vertically.
  • Segment BP is the third segment shown.

AM, MB and MP are also segments. There is also a line in this picture. It is labeled r.

Worksheet

Do the following Lines and Line Segment Worksheet to check that you have remembered what lines and segments are.

Angles

An Angle is a shape formed by two rays (or two line segments) that meet at a point. We will measure the size of the angle by using degrees. Here are some examples:
Acute-angle.jpg Right-angle.jpg Obtuse-angle.jpg

The right angle shown in the middle is a special case. If two segments or lines meet at a 90 degree angle we say they are perpendicular. In general we have the following cases:

  • Right angle - exactly 90 degrees
  • Acute angle - between 0 and 90 degrees. (the example shown measures 55 degrees)
  • Obtuse angle - between 90 and 180 degrees (the example here is 140 degrees)


When we write about angles we can use two different types of notation. They are both acceptable:

  • <ABC : The letter in the middle always gives the location of the point where the segments meet. B is called the vertex.
  • <B : Sometimes we just write the letter of the vertex of the angle.

Do the Angles and their Properties Worksheet

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