It extends indefinitely in all directions. Space is made up of all possible planes, lines, and points. In more obvious language, a plane is a flat surface that extends indefinitely in its two dimensions, length and width. All possible lines that pass through the third point and any point in the line make up a plane. A line exists in one dimension, and we specify a line with two points. The point of the end of two rays is called the vertex.Ī point exists in zero dimensions. Note that a line segment has two end-points, a ray one, and a line none.Īn angle can be formed when two rays meet at a common point. That point is called the end-point of the ray. A ray extends indefinitely in one direction, but ends at a single point in the other direction. We construct a ray similarly to the way we constructed a line, but we extend the line segment beyond only one of the original two points. On the other hand, an unlimited number of lines pass through any single point. For any two points, only one line passes through both points. You may specify a line by specifying any two points within the line. Like the line segments that constitute it, it has no width or height. Its length, having no limit, is infinite. A line extends indefinitely in a single dimension. The set of all possible line segments findable in this way constitutes a line. In this way we extend the original line segment indefinitely. Starting with the corresponding line segment, we find other line segments that share at least two points with the original line segment. The word plane is written with the letter so as not to be confused with a point (Figure 4 ).As for a line segment, we specify a line with two endpoints. A single capital letter is used to denote a plane. It is usually represented in drawings by a four‐sided figure. A plane has infinite length, infinite width, and zero height (or thickness). In Figure 3 , points M, A, and N are collinear, and points T, I, and C are noncollinear.įigure 3 Three collinear points and three noncollinear points.Ī plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. If there is no line on which all of the points lie, then they are noncollinear points. Points that lie on the same line are called collinear points. A line may also be named by one small letter (Figure 2). The symbol ↔ written on top of two letters is used to denote that line. A line has infinite length, zero width, and zero height. It extends infinitely far in two opposite directions. Figure 1 illustrates point C, point M, and point Q.Ī line (straight line) can be thought of as a connected set of infinitely many points. A point represents position only it has zero size (that is, zero length, zero width, and zero height). It is represented by a dot and named by a capital letter. Although these terms are not formally defined, a brief intuitive discussion is needed.Ī point is the most fundamental object in geometry. These terms will be used in defining other terms. Because that meaning is accepted without definition, we refer to these words as undefined terms. This process must eventually terminate at some stage, the definition must use a word whose meaning is accepted as intuitively clear. When we define words, we ordinarily use simpler words, and these simpler words are in turn defined using yet simpler words. Point, line, and plane, together with set, are the undefined terms that provide the starting place for geometry. Summary of Coordinate Geometry Formulas.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.
0 Comments
Leave a Reply. |