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1.2 Points, Lines, and Planes
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Terms
Description A point has no dimension (no length, width, or height). It does have a location, or position. How to Name It Name a point by a single capital letter. Example Point A or
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Terms
Description A line extends in opposite directions without end and has one dimension—length. It’s a set of points. How to Name It Name a line by a single lowercase letter or by any two points on the line. Example
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Undefined Terms
Description A plane is a set of points that extend in two dimensions (length and width, no thickness) without end. We represent a plane by a flat surface. How to Name It Name a plane by a single capital letter or by any three points on the plane (that do not lie on the same line). Example Plane P or plane ABC P
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Postulates
1.1 – Given two distinct points, there is exactly one line that passes through them. 1.2 – Given any three distinct points in a space not on the same line, there is exactly one plane that passes through them Student Activity Example – Page 12
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Postulates
1.3 – The line determined by any two distinct points in a plane is also contained in the plane. 1.4 – No plane contains all points in space.
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Ruler Postulate
Postulate 1.5 – There is a one to one correspondence between the set of all points on a line and the set of all real numbers. Notice that each point has one and only one number. One point to One Number. One-to-one correspondence. This postulate is demonstrated every time you use a ruler, yardstick or tape measure.
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Laws
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Laws
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Laws
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Drawing Lines
Perform parts a through d in order to create a single figure. a. Draw three noncollinear points, M, N, and L. b. Draw
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Using Postulate 1.2
Use the figure shown to answer the question. What plane contains points N, P, and Q? Shade the plane. Solution
The plane on the bottom of the figure contains points N, P, and Q.
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