1.1.1 Understanding Points, Lines, and Planes
Key Objectives • Identify, name, and draw points, lines, segments, rays, and planes. • Apply basic facts about points, lines, and planes. Key Terms • A basic geometric figure that cannot be defined in terms of other figures is an undefined term . • Points that lie on the same line are collinear . • Points that lie in the same plane are coplanar . • A segment or line segment is the part of a line consisting of two points and all points between them. • An endpoint is a point at the end of a segment or the starting point of a ray. • A ray is a part of a line that starts at an endpoint and extends forever in one direction. • Opposite rays are two rays that have a common endpoint and form a line. • A postulate , or axiom, is a statement that is accepted as true without proof. • An intersection is the set of all points that two or more figures have in common. Theorems, Postulates, Corollaries, and Properties • Postulate Through any two points there is exactly one line. • Postulate Through any three noncollinear points there is exactly one plane. • Postulate If two points lie in a plane, then the line containing those points lies in the plane. • A point names a location and has no size. It is represented by a dot. • A line is a straight path that has no thickness and extends forever. • A plane is a flat surface that has no thickness and extends forever.
• Postulate If two unique lines intersect, then they intersect at exactly one point. • Postulate If two unique planes intersect, then they intersect at exactly one line.
Geometry is an area of mathematics concerned with the study of two-dimensional and three-dimensional figures. Before a figure can be studied in geometry, even the most basic parts of the figure must be identified and named. For example, consider a triangle. A triangle is a very simple figure with three sides where each pair of sides meets at a corner. Even though a triangle is a simple figure, its parts must be identified using geometric terms before a triangle can be explicitly defined. The most elementary geometric figures are discussed in the examples below.
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