Start by familiarizing yourself with the concepts below.
Points
A point is an exact location on a plane. They are usually named with a single letter, such as point A, B, C, and so on.
Remember that points are places, not things. They are represented by a dot, but take up no space themselves.
Example of Points 
Plane
A plane is a flat two-dimensional surface that extends infinitely in every direction.
Planes may be named by giving them a capital letter, or by listing any three points on the plane in any order.
The plane in the example could be called Plane M, Plane ABC, Place CBA, Plane BCA, or any other combination of the three point names.
Points that are on the same plane are called coplanar points.
Example of a Plane 
Lines
A line is a straight path between two points, which extends infinitely in both directions. It has no width and therefore takes up no actual space. It's flat.
Lines can be named by drawing a horizontal arrow above two points in the line. For example, a line with points C and D would be written like \(\overleftrightarrow{CD}\) or \(\overleftrightarrow{DC}\)
They may also be identified using a single lower case italic letter, often written in cursive. So the line in this example could be called line \(\overleftrightarrow{CD}\), \(\overleftrightarrow{DC}\), or line l.
Example of line l 
Coordinate Plane
A coordinate plane, also known as a Cartesian plane, after a French mathematician, is a two-dimensional plane arranged in a grid-like structure. It consists of a vertical line called the y-axis and a horizontal line called the x-axis.
Points on a coordinate plane are assigned coordinates, which is a pair of two values given as an ordered pair (x,y), where x is the distance left or right of the y-axis and y is the distance above or below the x-axis.
A coordinate plane is arranged into four different quadrants, which are the different sections of the plane divided by the axes.
Coordinate planes must have some sort of scale, which is how many units one space on the grid represents. The scale in the example image is 1, since each block in the grid represents one unit. The scale is written along the axes of the plane.
In the example image, point A is at (-4,3) because it's located four spaces to the left (negative x), and three spaces up (positive y). Point B is at (4,2), because it's 4 spaces to the right of the y axis (positive x), and 2 spaces up (positive y).
The Cartesian/Coordinate Plane 
The Quadrants 
Collinear Points
Collinear points are points that are on the same line. In this example, points A, B, and C are collinear. Points C, D, and E are also collinear. Points A, B, and D are NOT collinear, nor are points D, E, and B.
Collinear points are part of the same line 
Line Segments
A line segment is a part of a line with two endpoints.
Line segments can be represented by drawing a horizontal line above two points in the line. For example, a line segment with endpoints C and D would be written like \(\overline{CD}\) or \(\overline{DC}\)
The length between two points in a line segment is simply the two points listed next to each other. So the length from C to D would be written: CD.
Example of line segment CD 
Congruent Line Segments
Line segments are congruent if they have the same length.
For example, a one foot line segment would be congruent with another one foot long line segment. In the example shown, \(\overline{AB} \cong \overline{CD}\). The equals sign with the little squiggle over it (tilde) means "is congruent to."
The little line going through the middle of each line segment are called tick marks. When tick marks match, it means the lines are congruent. Since line segments \(\overline{EF}\) and \(\overline{GH}\) both have two tick marks, we know they're congruent, even though I never specified an exact length.
Statements like \(\overline{AB} \cong \overline{CD}\) or \(\overline{EF} \cong \overline{GH}\), are known as congruency statements. We may need to write these in proofs, which we'll get into later on.
Congruency Example 
Rays
A ray is a part of a line that starts with one endpoint and extends infinitely in one direction.
Rays can be represented by drawing a horizontal arrow above the points in one direction. For example, \(\overrightarrow{AB}\)
It is best to start with the endpoint and extend the arrow right towards the other point. While \(\overleftarrow{BA}\) is technically correct, \(\overrightarrow{AB}\) is just a little easier to read since it goes left to right. So stick with notating it this way rather than right to left. In this example, \(\overleftarrow{AB}\) and \(\overrightarrow{BA}\) would be incorrect, as the arrow would go the wrong direction from A to B.
Opposite rays are two rays that start from the same point and go off in opposite directions. If point C lies between points A and B on \(\overleftrightarrow{AB}\), then \(\overrightarrow{CA}\) and \(\overrightarrow{CB}\) are opposite rays.
Example of ray \(\overrightarrow{AB}\) 
Parallel Lines
Parallel lines are lines that are always the same distance apart and never meet. They have the same slope.
They are shown by drawing two vertical lines between each line name, for example, \(l \parallel m\) means "l is parallel to m."
In this example, it could also be written \(\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}\)
Example of parallel lines l and m 
Perpendicular Lines
Perpendicular lines are lines that intersect at four right angles (ninety-degree angles).
They are shown by drawing a perpendicular symbol between each line name, for example, \(l \bot m\) means "l is perpendicular to m."
Example of perpendicular lines l and m 
