TenMarks teaches you about the basics of geometry.
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Learn the Basics of Geometry In this lesson, let’s learn about the basics of geometry. The problem wants us to use the figure to name each of the following and we are given this figure, which looks like there’s a plane Z and it’s got two different lines that intersect and a whole bunch of points on it. So let’s see what the problem wants us to do. It wants us to name each of the following, the three collinear points. Collinear points are points that lie on the same line. Which points lie on the same line here, which three points? Well, we can see A, B and E lie on the same line, so these are three collinear points. Remember, the points have no thickness. They are the smallest bits that you can occupy in space. Five coplanar points, when we look at the word “coplanar”, it means on the same plane, points on the same plane. As we can see, all of these points are on the same plane Z. So it looks like one, two, three, four, five, A, B, C, D, E—all of them lie on this same plane. Just to recall what is a plane, a plane is a flat surface with no thickness where lines and points appear, so all these lines and points are on the same line or on the same plane. Which plane contains E? Well, there’s only one plane here but if we look at this point, this is on this particular plane called Z. A line containing B and E—which line contains B and E? So the line that contains B and E—this is B and E, this is the line segment, right? But the line that contains it has no end points. Remember that a line extends indefinitely in both directions. This line is n. N is the line that contains both B and E as points. It also contains A, but a line extends indefinitely in both directions. What are rays? Rays are line segments that start at an end point and extend in indefinitely in one direction. So for example, C is a ray. A moving this way is a ray. E moving this way is ray. And A moving this way is a ray, so how many rays do we have? We have A—this ray. Actually, we can call it AB is a ray, AE is a ray. So we could see this is a ray because it heads in this direction, one end point, and extends. One end point, C, and extends. This is the ray. Then we have E extending in this way; that’s a ray. And we have A extending in this way, which is also a ray. All of these are rays. What are opposite rays? Opposite rays are like A extending in this direction, A extending in this direction. They are opposite rays because they extend in the opposite directions. For example, E in this direction and A in this direction are opposing rays. Line segments are parts of a line, so for example, BE is part of a line. Let me actually erase what we’ve done before so it becomes a little cleaner. If I look at line segments, BE is a line segment because it is a part of a line with two definite end points. AB is a line segment. You’ve got AC, which is a line segment, and you have AE, which is a line segment. Key things to remember when it comes to basic geometry, lines, points and planes, that’s the core of geometry, is if we have two points, there can only be one line, only one line that connects the two. If we have three points that lie on a line, all three points have to be on the same plane. And if things lie on the same plane, then they are on the same line and what have you, so it’s critical for us to understand what is a point, what is a line segment, what is a ray, and how they all fit into a plane.