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For a project I am considering on geometry in US high schools, I need a list of all the reasons that are usually allowed in two column geometry proofs there. I have a bachelor's degree in math and education.

Thanks in advance.

Dan

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  • $\begingroup$ When I was in high school, the rule was that we could use axioms and postulates from the book as well as any theorems from the parts of the book that had been covered in class. (And we could abbreviate "corresponding parts of congruent triangles are equal" as "CPOCTE".) Obviously, the "same" rule would mean something different in other schools that used other textbooks. $\endgroup$ – Andreas Blass Dec 13 '20 at 4:43
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We don't have any standards about that. The Common Core only specifies that students learn to do proofs about lines, triangles, quadrilaterals, and circles. Using two-column proofs isn't mandated, and neither are a list of which kinds of proofs you need to be able to demonstrate. Individual states can set that for themselves, but they may even push it down to individual districts or even individual teachers.

It's kind of a pain in the neck, to be honest. I live in New York state which has had a uniform final exam in geometry for the past 150 years or so. But I've never gotten a straight answer even in our state system of how many intermediate steps you need between knowing that two lines are parallel to knowing that their adjacent angles are congruent. Some people argue that you always need to say that the angles are right angles by "definition of perpendicular" and then conclude that they are congruent because "all right angles are congruent", but others say that's pedantry and you can say that all right angles are congruent in a single step.

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    $\begingroup$ What are the most widely used geometry textbooks in New York state? $\endgroup$ – Dan Christensen Dec 11 '20 at 18:44
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    $\begingroup$ @DanChristensen Couldn't begin to guess. Engage NY has course materials approved by the state, so you might look at engageny.org/resource/geometry-module-1/file/111916 on pp 7-9 and 13 for a sample of reasons they like. $\endgroup$ – Matthew Daly Dec 11 '20 at 19:11

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