Geometry Help: Proving Statements

Learning to prove statements in geometry can help you far outside the math classroom. All throughout life you will encounter situations in which you must use logical reasoning to solve puzzles or answer questions - it happens at work and in personal relationships. Here are some tips for mastering geometrical proofs.

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How to Solve Geometry Proofs

Geometry Vocabulary

In order to understand how to prove statements, it's important to have the key words from this type of math at your fingertips. The following vocabulary words are needed to advance in high school geometry.

Statement A statement in geometry is like a hypothesis in science. It's what you need to prove.

Proof This is what proves your statement. When you make a statement, you have to back it up with objective facts, and these are called the proof.

Counterexample This is a fact that demonstrates that a given generalization doesn't apply across the board. You may make a statement based on one or two specific examples that seem to indicate a pattern, but then a third example might go against what you thought. This third example is called a 'counterexample' because it runs counter to your earlier statement.

The Given These are the objective facts that you can use to support your conclusion or your statement.

Steps to Proving a Statement

You can begin by taking careful notes in class, and observing the way your teacher writes down geometrical proof statements. She may show a couple of different ways to write them out, and you may be expected to follow suit. You can also probably find examples with visual elements in your textbook.

You might be using a 2-column proof. In these types of proofs, you write the statements on the left-hand side and the reasons on the right-hand side. The reasons will likely be geometry properties, such as the reflexive property or the transitive property. The following steps can serve as general guiding principles for how to prove statements.

  1. First you have to write out your statement. This is where you use geometric language to describe a mathematical situation.
  2. Then, you have to back it up using given information. You normally write the given facts above the rest of the information you are providing. It helps if you can demonstrate this objective information in a visual display. Try drawing a figure or two above your statement to show given information.
  3. Keep going until you have explained every necessary aspect of your original statement using diagrams and given facts. This is also called proving a statement using logic.
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