Many students find geometry proofs intimidating and perplexing. They are faced with a problem and may not understand how to navigate a logical set of premises that go from the stated givens to reach the correct conclusion. Teachers also struggle with ways to make geometry proofs more accessible to their pupils. But there are strategies for approaching geometry proofs that focus on new, simpler ways to think about the problem, rather than concentrating on rigid formats.
Work backwards, from the end of the proof to the beginning. Look at the conclusion you are supposed to prove, and guess the reason for that conclusion. Use the if-then logic you are learning about to figure out what the second-to-last statement should be. Work your way through the problem back to the premise.
Approach the proof like a computer. This works especially well for formal two-column proofs. Computers must have access to every single step in the chain of logic. Every step must be expressed for a computer to understand it, even if the statement seems obvious. Writing a formal proof is like communicating with a computer.
Approach the proof as if you were a storyteller. If you're telling a story, you must include each part of the story in a logical, continuous, and chronological procession, or the story will make no sense. Read the problem, and tell yourself a story. Make notes and marks on a diagram or on scratch paper if you need to, to work through each step. When you understand each step and the order it must go in, then you can approach the formal proof and work your way through.
Approach the proof as if you're trying to solve a mystery. If you were a detective, you might survey the crime scene, gather the known facts, and write them down. Then, you would take the facts and go through them step by step to prove who committed the crime, documenting each statement with supporting evidence. This process is exactly what you need to do to solve a geometry proof -- but solving a crime can seem more interesting than working through a math problem.
Things You'll Need
- geometry image by Alexey Klementiev from Fotolia.com