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Geometry

This section introduces the fundamental concepts of geometry by defining points, lines, and planes and exploring related terms such as collinear, noncollinear, coplanar, noncoplanar, and intersections. It covers the basic properties of these geometric elements and their relationships, emphasizing the importance of precise definitions in geometry.

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Geometry

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  1. Geometry Points, Lines, and Planes Section 1-2

  2. This section establishes the basis for our study of geometry. As with all things, we start at the beginning and the definition of the point, the line and the plane is that beginning. You will increase your mathematical vocabulary by learning about space, collinear, noncollinear, planar, noncoplanar, and intersection definitions. …\GeoSec01_02.ptt

  3. There are three undefined terms in the study of geometry. From these three undefined terms, the body of geometry begins. These three terms are the point, the line, and the plane. …\GeoSec01_02.ptt

  4. Points are undefined and dimensionless. They have no size. We represent points with a dot on a surface and we name that point with a capital letter. A  ALL GEOMETRIC FIGURES CONSISTS OF POINTS. …\GeoSec01_02.ptt

  5. B  A  Lines are undefined and have one dimension, which is length. The geometric line is just like the algebraic line. It is defined by two or more points and it consists of all the points that are on the line. Lines are represented by a line with arrow heads on each end. This symbolizes that a line has infinite length. n It takes two or more points to define a line, thus a line will have at least two points on it as shown above. …\GeoSec01_02.ptt

  6. B  A  Unlike the line, a line segment has finite length. The line segment is a section of a line. It has endpoints. If two or more points are on the same line, then the points are said to be collinear. Therefore, if two points are collinear, then they are on the same line. If two points are not on a given line, then they are said to be noncollinear. …\GeoSec01_02.ptt

  7. D  A  R C  B  A plane is defined by three noncollinear points. These three points are defined as coplanar. A plane is like the surface of a floor. A plane has width and length, but no depth. A plane’s surface is populated with an infinite number of points. Below, pointsA, B, and C are coplanar. If a point is NOT on the plane, then it is called noncoplanar. Point D is noncoplanar with plane R. …\GeoSec01_02.ptt

  8. E  F  D   C   A B N Space; the boundless, three-dimensional set of all points. …\GeoSec01_02.ptt

  9. m T  m P  l m m  l B  R  P N A The intersection of two figures is the set of ALL points that are contained in both figures. …\GeoSec01_02.ptt

  10. Summary: This section covered the point, the line, and the plane. We found that all geometric figures consists of points and that the intersection of geometric figures is a set containing all points common to both figures. We discovered the finite length of line segments, as well as definitions related to points, lines, and planes. Briefly, we touched on the concept of space figures. …\GeoSec01_02.ptt

  11. END OF LINE …\GeoSec01_02.ptt

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