It also works backwards. If we have points going due left, then we can also have points that go the opposite direction, straight right. Lines are indefinite, by the way. Later in the section, titles "Initial Postulates and Theorems You Should Know", we'll introduce a very important theorem that involve points and theorems. Plane: A plane is the same as a line, except you have points everywhere, and the points don't go in one specific direction. It's a whole field of points. Line Segment: A line segment is just part of a line.
Remember above when I said that lines are indefinite, and that they keep going and going? Line segments stop somewhere in both directions.
Ray: A ray is like a line, but the line takes off in one direction to infinity while the other side is like a line segment. The end of the line is called the endpoint. Opposite Rays: Two rays that share the same endpoint that take off in opposite directions. The rays would create a line. Angle: Two rays that share the same endpoint, however, the rays take off in different directions.
The area in the middle of the two rays is the angle measure. Ready to test your knowledge? Try a Problem Set. Give an example of an undefined term. What makes this term hard to define? Give an example of a defined term.
A line goes out infinitely past both points, but in geometry we symbolize this by drawing a short line segment, putting arrowheads on either end, and labeling two points on it. The line is then identified by those two points. It can also be identified with a lowercase letter. A plane is described as a flat surface with infinite length and width, but no thickness.
It cannot be defined. A plane is formed by three points. For every three points in space, a unique plane exists. A symbol of a plane in geometry is usually a trapezoid, to appear three-dimensional and understood to be infinitely wide and long.
A single capital letter, or it can be named by three points drawn on it. Modeling a plane in everyday life is tricky. Nothing will accurately substitute for a plane, because even the thinnest piece of paper, cookie sheet, or playing card still has some thickness. Also, all of these objects end abruptly at their edges.
Planes do not end, and they have no thickness. A set can be described as a collection of objects, in no particular order, that you are studying or mathematically manipulating. Sets can be all these things:. Or if you have some sort of smaller letter over here, we can call this Line L. But notice how I'm writing the arrows above my letters; I have arrows on either side.
And these arrows tell you, the geometry student, that it extends infinitely in this direction. Now this arrow here extends infinitely in that direction. You can have points be collinear, that is, they share the same line.
So here we could have, C, D, and E are all collinear. And if you look at Point F here, I drew this in to draw a contrast.
So the three key terms that are not definable, but only describable, are the line, which is a set of points extending infinitely in one or the other direction; plane, which is a flat surface with no thickness; and the third undefined term is point and that has a location and no size.
Brian McCall. Next video playing in 10 Counterexample - Concept Cancel. Brian McCall Univ. Explanation Transcript In Geometry, we have several undefined terms: point, line and plane. Start on. Show related SlideShares at end. WordPress Shortcode. Next SlideShares.
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