What Are Points, Segments, Rays, Lines And Midpoint Explained Collinear Points And Concurrent Lines
In this video we discuss what are points, segments, rays lines and midpoints in geometry. We go through examples of each and also discuss collinear points and concurrent lines.
Transcript/notes
In geometry a point is represented by a dot, such as point A. It has no dimension or direction, and is typically labeled by a capital letter.
Now, if we have 2 points, point A and point B, and we connect these points with a straight line, this is a segment, or a line segment. The 2 points at the end of the segment are called end points of the segment and these are used to label the segment. The segment AB is symbolized by the capital letters of the endpoints with a line above the letters, as you see here. And the segment can also be written as segment BA, so segment AB is the same as segment BA.
One special point on a segment is the midpoint, which is the point that is halfway between the endpoints. On our example segment AB, the midpoint is here, and we can label it as M. Since the midpoint is the same distance from the endpoints, we say it is equidistant from the endpoints. To show this on the segment, we will put these tick marks on segment AM and segment MB, and we know that AM equals MB.
Now let’s go back to segment AB. If we extend, going past B and put this arrow on the end, which means this goes on forever, we have what is called a ray. And this ray is symbolized by the capital letters AB with a line with an arrow at the end that extends past the endpoint, and this is called ray AB. When we symbolize a ray, such as ray CD, we always start with the starting point, or origin. One note, the ray AB is not the same as the ray BA, as they have different starting points and extend in different directions.
Again, let’s go back to segment AB. This time we are going to extend past both endpoints of the segment, again, with arrows at the end to go on forever.
This is now a line, symbolized by the capital letters AB with a line with arrows going in each direction above the letters. And, like segments, this line can also be written as line BA, so line AB is the same as line BA. And sometimes, a single lowercase letter is used to describe a line, such as line t.
Two other terms that are important to understand are collinear points and concurrent lines.
Collinear points are points that lie on the same line, for instance, the points A, B, and D are collinear points and the point C is not a collinear point with a, b, and d. And concurrent lines are 2 or more lines that all pass through the same point, as you see in these examples.
Timestamps
0:00 What are points in geometry explained
0:12 What are line segments explained
0:35 What is a midpoint explained
1:00 What are rays in geometry explained
1:30 What are lines in geometry explained
1:59 What are collinear points and concurrent lines explained
