Geometry for Elementary School/Lines

From Wikibooks, open books for an open world
Jump to navigation Jump to search
Geometry for Elementary School
Points Lines Angles

Lines[edit | edit source]

A line is as wide as a point, infinitely thin, having an infinite number of points, (in a straight row), extending forever in both the directions. Remember that this is impossible to be constructed in real life, so usually we would simply draw a line (with thickness!) with an arrow on both ends. Any two lines can intersect at only a single point. Lines that are on the same plane are 'coplanar'.

Geom lines lines 01.png
Geom lines lines 02.png

Line segments[edit | edit source]

A line segment, or segment, is a part of a line, which has two endpoints. The endpoints give the line segment a fixed, or finite length.

Geom lines seg 01.png
Geom lines seg 02.png

Line segments AB, and CD, can bewritten as , and

Geom lines seg 03.png
Geom lines seg 04.png
Geom lines seg 05.png
Geom lines seg 06.png

Rays[edit | edit source]

A ray is a line segment that has only one endpoint. A ray is infinite in one direction. That means that it goes on forever in one direction. As they are impossible to construct in real life, usually we will just draw a line with an arrowhead on one end. They can be expressed as .

Geom lines ray 02.png

Intersecting lines[edit | edit source]

Two lines intersect when they cross each other. They form vertically opposite angles, which we will learn later. The point where the lines intersect is called the point of intersection. If the angles produced are all right angles, the lines are called perpendicular lines. If two lines never intersect, they are called parallel lines. Parallel lines will be discussed in detail later. Usually if two lines are not parallel, they intersect each other. The definition of intersecting lines can be called two lines that cross each other a only one point. This point is called the point of intersection.

Axiom: there is only a single straight line between two points[edit | edit source]

Axiom: there is only a single straight line between two points.

Geom lines axiom 1.png
Geom lines axiom 2.png
  • show by halving that there are infinite number of points in a line
  • show that the number of points in a long line and a short line is equal