How to Solve Geometry Proofs

The purpose of geometry is to be able to show what you have learned through constructed written logic, called a proof. A geometry proof's purpose is to work from a hypothetical theory to a conclusion. This can be thought of as a pyramid. You start with a base belief, prove it, then start with another belief. Although there are numerous geometry proofs, there are a few universal steps needed to solve them.

Difficulty:

Challenging

Instructions

Things You'll Need

• Paper
• Pencil
• Graphing calculator

1. Read the problem and then re-read it. Make sure you have a good understanding of the information given to you.

2. Write down the givens. This is the information given to you. Both you and the reader know that your givens are correct.

3. State the theorem, or what you need to prove. It is important that you start by determining what you need to find.

4. Make sure there is a graph, so there is visual representation of what you are going to prove. Make it large enough that you can see it and work on it. Be sure to label all the points with the correct letters. Make sure that you mark parallel lines or congruent angles.

5. Determine how you are expected to answer. Is your proof expected to be done in a two- column chart, a collegiate paragraph form or a mixture? If it is supposed to be a two-column chart, mark the left-hand column labeled "statements" and the right-hand column "reasons."

6. Work the proof. Each statement should have a reason. If the statement is given in the problem or drawing it, simply write "given." If not, work though that statement with definitions and proven theorems for the reasons.

7. Check your last sentence. The last sentence in your proof should match your theorem statement.