Geometry Proofs...Help!!

[Based on Faith Academy]

Hello All!

Let me just say, I love math. My daughter says I smile when I grade her school. For the life of me, I have never been able to wrap my head around geometry proofs. I get learning the definitions, theorems, and postulates. What I don't get is if there is an order to put them on the paper. To me, it would seem to be more like if then statements, but when I look at people's proofs they don't seem to follow a format. 

 Trying to explain them to my daughter is like speaking a foreign language. At least when my son did them, I knew he had some idea. With my daughter, she is not math minded. 

Help me understand them so I can help her, please. If there is a book or a website, that would be fantastic. 

TIA,

Christina

[EKS]

Most proofs have more than one way they can be written, but the solution manual will have just one.  When you grade geometry work, you have to know if what the student has produced is an acceptable alternative.  Is this perhaps what you are having trouble with?  Could you give an example?

[Based on Faith Academy]

Yes. To me there are multiple ways to prove something with all the theorems and what not. What order do they go in? How do I know that I am proving it?

Ex..

Given: angle B is a right angel; line segment AB is parallel to line segment DE

Prove: triangle DEC is a right triangle

 

[EKS]

19 minutes ago, Based on Faith Academy said:

To me there are multiple ways to prove something with all the theorems and what not.

This is usually true.  

19 minutes ago, Based on Faith Academy said:

What order do they go in? 

You choose an order that ensures that each thing follows logically from something already stated in the proof.  

21 minutes ago, Based on Faith Academy said:

How do I know that I am proving it?

This is where experience and expertise come in.  

23 minutes ago, Based on Faith Academy said:

Ex..

Given: angle B is a right angel; line segment AB is parallel to line segment DE

Prove: triangle DEC is a right triangle

Could you give how you would prove this and how the solution manual proves it?  That would allow me to understand whether your proof is equivalent to the solution.

Also, a diagram (or more information) is necessary because, from what you've stated here, the relationships between the points aren't clear.  

[daijobu]

In writing a proof, whenever I make a statement, I ask myself, "How do I know this to be true?"  If 2 segments appear to be the same length, and knowing they are the same is important to proving something, then I ask myself, "How do I know they are the same length?"  Hint:  it's usually congruent triangles, lol.  But then I ask myself, "How do I know they are congruent?"

[Not_a_Number]

A proof is just an airtight logical explanation. You can write proofs equally well in all parts of math: there's nothing special about geometry. It just seems to be where people see proofs. 

[Jann in TX]

When I teach proofs I insist that my students mark up their diagram as they go.  This is IMPORTANT as it allows the student to see what has been 'stated' or 'proven' so far in the problem.    All statements made must be backed up by the diagram.  Just doing this helps the progression of the proof!

 

[lmrich]

When my dd struggled with geometry proofs, I found some cut and paste geometry proofs for her to do; it helped. I also would give her a  list of the theorems and postulates that could be used in the proof. She is very visual so it really helped her to see it. I also added in more proofs that her curriculum required as she needed more practice. I think we spent two weeks, just 15 minutes a day, practicing proofs, before she felt confident. And I agree with Jann - draw and mark up every diagram. (I am currently working with a kid who was CP and has poor fine motor control; geometry is extremely hard for him because he can't draw and mark it up)

[EKS]

Both of my kids struggled with proofs, and what helped them was for me to sit with them--FOR WEEKS--and talk them through it.  

That said, it's important for the instructor to have a pretty good handle on proofs themselves for this method to work.

And all of that said, I decided to farm out the grading for my younger son because of the issues that the OP has identified here. We used Derek Owens, but I wouldn't recommend his geometry course for a struggling student.