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Two-Column Proofs

Geometric proofs are among the building blocks of math. Learn how to use two column proofs to assert and prove the validity of a statement.

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Give Me One Reason

Credit: polandeze
Source: http://www.flickr.com/photos/polandeze/1206596658/
License: CC BY-NC 3.0

Have you ever tried to convince a friend to see things your way? You can’t change minds unless you give people a reason to agree with you. If you back up each of your statements with a strong, fact-based reason, people will be more likely to see things your way.

Opinions and Facts

If you watch political speeches, you′ll notice that politicians often try to pass their opinions off as facts. Instead of “I think we should lower the maximum speed limit,” a politician is more likely to say: “We must lower the maximum speed limit.” Advertisers also voice opinions without giving reasons for them. They make statements like: “Our dog food will make your pet healthier, happier, and more energetic." But they don’t explain why.

Credit: Beatrice Murch
Source: http://commons.wikimedia.org/wiki/File:Mauricio_Macri_-_the_politician.jpg
License: CC BY-NC 3.0

There’s one more step to building a good argument. You have to make sure that the reasons you give are true. If your reasons aren’t built on fact, your arguments might be convincing, but they’ll also be wrong.

In a two-column proof, you know your reasons are correct because you’ve proven them before. In real life, arguments can be much messier. In fact, some people use false reasons to trick people into believing things that aren’t true.

See for yourself: http://zapatopi.net/treeoctopus/

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If you learn to back up your statements with reasons, people will be more likely to agree with you. Even a simple lunchtime argument about a sports star becomes more convincing when you provide reasons for your belief. 

What sorts of facts does the author of the article below use to back up his statements about baseball players?


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  1. [1]^ Credit: polandeze; Source: http://www.flickr.com/photos/polandeze/1206596658/; License: CC BY-NC 3.0
  2. [2]^ Credit: Beatrice Murch; Source: http://commons.wikimedia.org/wiki/File:Mauricio_Macri_-_the_politician.jpg; License: CC BY-NC 3.0

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