How do you study for deductive geometryI don't understand how to prove.

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Even if you struggle with proof, you can and should study. While you may never find proof to be easy, if you do not master the basics you will never be able to do proofs.

(1) Know the definitions -- really know them. What is a ray? If you don't know, then the definition of an angle (comprised of two rays with a common endpoint) becomes impossible, etc...

(2) Know the postulates and/or axioms. Even if you are not required to memorize them, you need to know them. In fact, just memorizing isn't all that helpful; different texts will word things differently. Understand what they mean.

(3) Know the theorems that you have learned -- again memorizing gets you so far, but understanding what they are telling you is important. Know the conditions that must be met (e.g. the pythagorean theorem only holds for right triangles in a Euclidean plane)

(4) Be sure you are able to read diagrams correctly -- what information is being conveyed, what information you can infer (e.g. that given points are collinear, etc...) Know what the markings mean.

You will need to try proofs; it might take weeks of work before you finally get what is going on. Read the proofs in the examples-- can you find a different way to prove it? (A proof is just a logical argument -- master this and you will find that making persuasive arguments in any other field is much easier.) There are many tips for proofs -- working backwards (what do I need to show this), looking for a similar problem, etc... Unless you are trying on your own, watching someone else do proofs will have very little benefit. If you are just watching, at least ask why the person is making each statement.

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