9.1 Points, Lines, Planes, and Angles Part 1: Points, Lines, and Planes.

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Presentation transcript:

9.1 Points, Lines, Planes, and Angles Part 1: Points, Lines, and Planes

Points, Lines, and Planes The most basic ideas of geometry are points, lines, and planes, though it is not really possible to define them. – A point has not magnitude or size. – A line has length but no width and extends in two directions without end. – A plane is a flat surface and extends in all directions without end.

Parts of a Line NameIncludes…FigureSymbol Line AB or BA…all points on the line, including A and BAB or BA Half-line AB…all points from A through B and so onAB Half-line BA…all points from B through A and so onBA Ray AB…point A and all points from A through B and so onAB Ray BA…point B and all points from B through A and so onBA Segment AB or BA …points A and B and all points between A and BAB or BA  

Recognizing Types of Lines  Write each of the following using the correct notation. Then name the points included in it. A B C D ray BCline segment AD half-line ADray DA line segment DA

Sets Lines, rays, half-lines, and segments may be considered sets of points. The intersection (symbolized  ) of two sets is all the elements they have in common. The union (symbolized  ) of two sets is all the elements found in at least of the two sets.

Identifying Elements of a Set Based on the figure below, specify each of the sets given in a simpler way. AB  BC  AC  CA CD  C  BD  CD A B C D 

Intersections Parallel lines lie in the same plane and never meet. – In the example, ℓ 1 || ℓ 2. – Parallel planes also never meet, no matter how far they are extended. Intersecting lines do meet at one point. – Intersecting planes form a straight line (the one and only line they have in common). Skew lines do not lie in the same plane and never meet.