Help with Geometry proofs, please.

[HSKLNG]

My dd is having some challenges with this. She says she gets it and when she has "prove" the statement it seems to me like she is just guessing.

 

Have you encounter a book or curr. that explains clearly and simply the why and when of the proofs.

 

She is using Classmates CD's, Life of Fred right now. One helps the other, but still...I even have couple more Geometry curr.

 

Does not matter how much or how many material I have as long as she really "get it".

 

Any ideas?

 

Thanks in advance.

[Maura in NY]

I'm assuming we're talking about 2-column proofs. Is that correct?

 

Could you give an example of a problem and her guess?

 

There is sometimes "guessing" involved in proofs. Often there is more than one way to prove what is being asked, and sometimes I can't see the whole path until I get started. So I prove what I know, and that takes me a little farther down the path...and I can see something else I can prove...sometimes it's a dead end and I have to back up. So maybe your daughter does understand, but doesn't have the light-bulb moment of clarity to see all the way through to the end of the proof before she begins.

 

In order to see the path at all, first you have to understand the logic of hypothesis/conclusion and the idea that each statement needs a reason. You have to know all the definitions, axioms, postulates and theorems that have been covered by your text up until the proof you are being asked to provide. If your daughter can't pull these up to apply them, then it will be difficult for her to do proofs.

 

She could take a look at this site:

http://www.themathpage.com/aBookI/plane-geometry.htm

(It lists the proofs in paragraph form, which isn't quite as easy to see as 2-column proofs - Try this one:

http://www.regentsprep.org/rEGENTS/mathb/1c/WhatPrf.htm)

 

Maura

[Claire in NM]

It might help if you had your daughter explain the proof to you. If she is getting it, then she should be able to express her proof orally. If she is having problems with proofs, here are some suggestions.

 

First of all, as you are working through the material, it is always good to have an index of the definitions, postulates, theorems, etc. when working on proofs. The repetition of having to look up the definitions, postulates, theorems, etc. helps in memorizing them.

 

When we approach a proof, we usually start with the given statement and determine how this information might lead us to the prove statement. Sometimes it works, sometimes it doesn't.

 

And sometimes it helps to work backwards. For example, I look at what I have to prove and ask, "What conditions have to be true to end up with the prove statement?" If two triangles are congruent, I ask myself which theorem can get me to the prove statement. Is it ASA, SAS, HL, ...? As I go through each, I look for congruences of sides and angles. Do not work the proof backwards, since wrong statements can be made. However, you can work backwards just enough to give you a hint as to how the proof will progress.

 

 

As for geometry, I would have to say Teaching Textbooks Geometry. They might have a couple of demos on proofs. The lecture CDs are a big help. On the other hand, there are some who feel that this course is not rigorous enough. This would imply that the level of comprehension of this material must be good.

 

Personally, for deductive geometry, I know that this curriculum is a good one.

 

Wishing you the best in your endeavor of proofs,

 

Claire in NM

[covenant.christian]

Teaching Textbooks. Great stuff there!