Geometry is all about figures, rules, and logical thinking. You need to learn the rules and properties of each figure and angle. There are a lot of them, but every rule is fair game on the exam.
Geometry is always a logical puzzle. The GRE gives you a tiny piece of information pertaining to a specific figure, and you must use your knowledge of the rules of the figure to logically infer the correct outcome. Geometry questions require you to state a series of “if…then” statements, constantly building to the correct answer.
In general, then, we have only one piece of advice. Don’t try to figure out the answer before you get there. You may not see the direction the logic will take you as you figure out a question. Rather, at each stage, jot down everything you know about the question. Piece by piece, you should get to the right answer.
II. Lines and Angles
The most basic element in geometry is the point:
If we have two points, we can connect them to form a line:
When two lines originate from the same point, they form an angle:
The point of intersection is the vertex and the two lines form the sides of the angle. The angle is designated in a number of ways. It is BAC where the middle letter is the vertex, A where A is the vertex, or x where x is located inside the angle.
Angles are measured in degrees, denoted by this symbol: °. For example, a 30 degree angle would be written as 30°.
When placed next to one another (or adjacent),
angles can be added up.
The sum of x + y here is 90°.
The sum of x + y here is 180°. Notice that x and y create a straight line. All straight lines are 180°.
Example 1
A beam of light is shown in the figure to the left reflecting off a mirror. What is the value of x?
Solution
x
= 36
Because these three angles form a straight line, they must add up to 180°. Therefore
BAC where the middle letter is the vertex, 
