Introduction to Points, Lines, & Planes

1. Introduction to Points, Lines, & Planes Vocabulary and Notation

2. Point, line, and plane • In geometry, the terms point, line, and planeare accepted as intuitive ideas and are not defined. • Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry. Although you cannot define undefined terms, it is important to have a generaldescription of their meanings.

3. Point • A point indicates a location and has no size. • A point is like a star in the night sky.  It is a little spec in a large endless sky.  • However, unlike stars, geometric points have no size.  Think of them as being so small that they take up zero amount of space. • Although a point doesn’t have any size, it is often represented by a dot that does have some size. • You usually name points by capital letters. • All geometric figures consist of points. http://www.gradeamathhelp.com/undefined-terms-in-geometry.html

4. Line • A line is represented by a straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points. • A line is like the edge of a ruler, that never ends. If you take a ruler and draw a line, imagine if that line kept going straight forever.  • The line you have is thick enough for you to see, but you need to imagine that your line is so thin that you can't see it - it has no thickness at all.  That is a geometric line. • Often a line is referred to by a single lower-case letter. • You can also name a line by its points. http://www.gradeamathhelp.com/undefined-terms-in-geometry.html

5. Plane • A plane is represented by a flat surface (like a piece of paper)that extends without end and has no thickness (just like the line). A plane contains infinitely many lines. • A plane is a flat piece of land (like a football field) that extends forever.  • Imagine that you can pick that football field up, and put it anywhere in the air that you like.  You can even turn it side ways, or diagonally.  • Although a plane has no edges, it is usually represented by a four-sided figure. • We often label a plane with a capital letter or by naming any three points in that plane. http://www.gradeamathhelp.com/undefined-terms-in-geometry.html

6. Collinear Points- points that lie on the same plane are collinear points. • Coplanar – points and lines that like in the same plane are coplanar. All the points of a lineare coplanar. • Space – space is the set of all points in three dimensions. • Intersection – when you have two or more geometric figures, their intersection is the set of points the figures have in common.

7. Segment - A segment is part of a line that consists of two endpoints and all points between them. • Ray – the part of a line that consists of one endpoint and all the points of the line on one side of the endpoint • Opposite Rays – opposite rays are two rays that share the same endpoint and form a line. • Angle – A figure formed by two rays that have the same endpoint

8. Coordinate – the real number that corresponds to a point is called the coordinate of the point. • Distance – the distance between points is the absolute value of the difference of their coordinates. • Congruent segments – When numerical values have the same value, you say that they are equal (=). Similarly, if two segments have the same length, then the segments are congruent () segments. • Midpoint - The midpoint of a segment is a point that divides the segment into two congruent segments. • Segment bisector - A point, line, ray, or other segment that intersects a segment at its midpoint is said to bisect the segment, therefore called a segment bisector.

9. Postulate or axiom • A postulate or axiom is an accepted statement of fact. Postulates, like undefined terms, are basic building blocks of the logical system in geometry. • Postulate 1-1: through any two points there is exactly one line. • Postulate 1-2: if two distinct lines intersect, then they intersect in exactly one point. • Postulate 1-3: if two distinct planes intersect, then they intersect in exactly one line.

10. Postulate 1-4: through any three noncollinear points there is exactly one plane. • Postulate 1-5 (Ruler Postulate) – every point on a line can be paired with a real number. This makes a one to one correspondence between the points on the line and the real numbers.