What are geometric proofs?

Geometric proofs are the process of proving a mathematical statement about a geometric figure by using theorems, postulates, definitions and axioms. They are an essential part of learning how to think about geometry and apply what you learn to other areas of mathematics.

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What are the different types of proofs?

There are three basic types of proofs: paragraph, flowchart and diagram. Each type of proof requires the student to explain their reasoning step by step and use concrete evidence to prove their claim. 

Paragraph proofs (sometimes called “two-column” proofs) are a common format seen in high school textbooks and are a good way to teach students how to write effective proofs. They contain a list of statements in one column and reasons for each statement’s truth in another column. 

A paragraph proof has to be written in chronological order, showing that each step allows the next statement to be true. Each step must be supported by a definition, theorem or property, and each of these must build on the previous statement. 

Flowchart proofs are an alternative to paragraph proofs and are a great way to teach students how to explain their reasoning in a more visually appealing manner. They usually use boxes to show each statement and arrows to show how the statements relate to each other. 

The three most important lessons students can learn from geometric proofs are: 1. Identify a clear goal, 2. Explain their reasoning step by step and 3. Support each claim with concrete evidence.