How to Learn Geometry Proofs

Proofs are the backbone of geometry.

Geometry proofs are the backbone of geometry. They are what give us evidence for the way geometry works. For instance, they explain why isoceles triangles always have equal angles at the base of the two congruent sides or why two equal right triangles always make a square. Written as a two-column chart, the first column of a geometry proof is dedicated to the statements based on observations of the given, while the second column is dedicated to the theorems that back up the statements in the first column. If you're confused about geometry proofs, you're not alone. However, this doesn't mean you can't learn them.

Things You'll Need

• Paper
• Pencil
• Geometry hypothesis
• List of geometric theorems

Instructions

1. Make up the theorem you are trying to prove. Make a statement you are going to use your knowledge of geometry to prove as factual, and write this at the top of your page.

2. Make statements on what you already observe. In other words, with the geometric shapes you have been given in the theorem, write the given observations of what could possibly help you solve the proof in the first column. In the second column, state the theorems from your list that make these observations true.

3. Edit your given shapes to help come up with theories that will lead you to solve the proof. Draw lines through them to make new shapes and angles to help solve your theorem.

4. Use the edited shapes to make more statements that will help solve your theorem. Once again, use your list of geometric theorems to back up your statements.

5. Keep repeating steps 3 and 4 until your theorems and logic bring you back to the statement you are trying to prove. Once you reach the statement you are trying to prove within your proof, assuming you have used evidence for every step you have taken, your proof will be done.

Tips & Warnings

• Geometry is about logic, so make sure you do your proofs in a logical manner. For instance, if you are trying to prove how two triangles with equal angles and different line lengths are always going to be similar, it is not necessary to divulge into theorems about rectangles.

• Pretend you are a lawyer in the court of geometry who is trying to testify on why your theorem is right. This means you have to use logic and evidence.

• Don't dig yourself into a dead end. If you use the wrong theorems to help solve your proof, you might put yourself in a place where your proof cannot be solved with the logic you have used, which means you will have to start over from scratch.

References

• For Dummies: Mastering the Geometric Proof
• TheMathLab.com: How to Write a Good Proof