Points are marked with a dot (any size), and are notated with a capital letter.
Points on a map are a great example because these dots represent locations. They are not accurate in terms of size, as you know a location on a map is not as small as the dot you can draw with a pencil.
Lines – infinite collinear points, extending forever in opposite directions.
Two (or more) points are required to create a line.
Notation (label):
Two capital letters with an double arrow on top.
The SAME two capital letters (in reverse order) with a double arrow on top.
An italicized lowercase letter.
Since lines are infinite, they can only be represented in our world by objects. In reality, they would go on forever into the universe.
Lines (represented) in the real world: football field.
Lines (represented) in the real world: railroad tracks and power lines.
Planes – infinite collinear points or lines that extend in all directions; however, only existing in two dimensions: length and width).
Three or more points are required to create a plane.
Since planes are infinite, they can only be represented in our world by objects. In reality, they would go on forever into the universe.
Planes (represented) in the real world: tile floor.
Planes (represented) in the real world: dirt field.
Rays – part of a line, starting in one location and continuing forever in the opposite direction.
Like a line, it has ONE dimension: length.
Notation (label): Two capital letters, starting with the endpoint letter. Arrow on top, always pointing to the right.
ALWAYS start notation with the endpoint (starting location) and draw your arrow on top, facing to the right.
Line Segments – a finite (measurable) part of a line with two endpoints.
Lines are one dimensional, so line segments are also one dimensional.
Notation (label):
The segment itself: two capital letters (endpoints) in either direction, with a bar on top (NO arrows).
The measure of the segment: two capital letters (endpoints) in either direction, WITHOUT a bar on top.
Intersecting Lines
Two or more lines that cross one another at ONE location (a point).
These two lines intersect at point M.
Intersections in the real world: street crossings.
Intersecting Planes
Two or more lines that cross one another at ONE line.
Intersecting planes at line AB.
Multiple planes intersecting: each intersection is a line.
Intersecting planes in the real world: boxes! Boxes are representations of intersecting planes. Remember, planes are actually infinite in length and width.
Angles – two rays that come together at ONE point, with an opening that can be measured in degrees (on a protractor).
A slice of pizza has a measurable angle! This is a representation because the rays are not infinite on a pizza.
Stairs are formed by right angles. The railing represents an obtuse angle, and the bricks are created with right angles.
In this example, the angle of elevation is a measurable, acute angle. The degree of measurement from the ground to the top of the tree is represented by the letter x.
This is a protractor. It can be used to measure angles from 0 to 180 degrees.
