Geometry Help

[4poobear]

My daughter is using Teaching Textbooks for Geometry and understands most of the concepts and can work the problems except doing proofs. I have watched the cds for the proof explanations and I can not grasp what theorem or postulate to use either. It is not that we don't understand the theorems, postulates definitions, etc., it is when to know why you use one over the other next in the proof. Any suggestions? i am at the point of hiring a geometry tutor in our area and they are not cheap!:tongue_smilie:

[Julie in MN]

To me, the biggest thing is to have a "plan." How are you going to accomplish the task?

 

For instance, my son keeps wanting to use SAS to prove two triangles are congruent, and yet he has not actually shown anything about a single "angle." So, if the plan is to use SAS, then he needs to show 2 sides are the same, 2 more sides are the same, and 2 angles in between are the same... therefore, SAS. Otherwise, he needs to make a different plan (such as SSS)!

 

I don't think the student's answer has to match the answer key, but I do think they need to cover every step leading to their "proof."

 

Does that help at all?

Julie

Edited January 4, 2011 by Julie in MN

[Maverick]

I agree--writing proofs takes practice, but it helps to keep the end in mind. If I'm given some information about two triangles and asked to prove them congruent, I have to use SAS, ASA, or SSS (which one do I have the info to use?). If I'm trying to prove a pair of sides or angles in those triangles congruent, I will likely need to use Corresponding Parts of Congruent Triangles are Congruent for the next step after proving the triangles congruent. Skim through your list of theorems and postulates and see which give you the "result" you're after.

[Susan C.]

You may need to get the tutor..... we did geometry last year. We started with Chalkdust, and wrote to Dana Mosely regularly with our proofs. There are several acceptable ways to do each proof, so you need someone to show them to if they don't match the key. We did change to BJU w/dvds, there was a 45 minute class to watch every day, and there was a ton of help with that. We wouldn't have survived without either and are very glad to have geometry behind us!

[creekland]

Is there anyone you could run a proof by that isn't as expensive as a tutor? There generally isn't just "one" way a proof can be done, but you have to know what is acceptable as a difference and what isn't. It's possible the way your or your daughter are "seeing" the proofs is equally as acceptable.

 

I know in our church I often help kids with simple math questions (or science) for free after church. Can you check there to see if anyone is a math person and can look at any proofs?

[MomsintheGarden]

You might want to try walking her through the proofs yourself. Look at the solution manual while helping her with each step. Talk about what she is to prove and ways to accomplish the goal. Draw a clear picture. Yes, I know there is a picture in the book, but it helps (BTDT). Have her do the proof the way the SM does it, just to make it easier on you, but if she is solid on doing something different and can support it, let her.

 

Yes, this can be excruciating, not to mention time-consuming, but it worked for us. I did this with my oldest, who was reluctant to do proofs in 9th grade but is now a math major.:) You will learn some geometry, too!

 

GardenMom

[Jann in TX]

I begin with fill in the blank proofs-- usually the statements filled in and the Reasons blank.

 

I then progress to 'mixed' blanks-- some statements and some reasons blank.

 

For a change I will mix up the statements and reasons in a proof for the student to put in order. I've found this to be a great way to teach proofs-- the student has limited options (thus more security)---and they have to think logically in order to put the proof in an acceptable order.

 

With many proofs there are numerous ways to work them correctly-- and the way one text teaches them may be completely DIFFERENT from another text! Proofs are not standard (in details) but they are standard in organization (formal proofs).

 

I worked one proof with my Geometry class today that EASILY had at least four different options (EQUALLY CORRECT) and it was only a 5 step proof!

[MyThreeSons]

Others have given some good tips. One other thing I tell my students is that sometimes you can start from both ends and work towards the middle. In general:

 

Always start by listing the given information.

Always finish with the statement that you are asked to prove.

Use the topic of the chapter you're in to give you an idea of where you're going. If you're in the chapter about SAS, ASA, etc. triangle congruencies, then you're likely to need to find some congruent triangles using those theorems.

You can only use CPCTC as a reason for saying that either a pair of angles or a pair of sides are congruent AFTER you have established that those elements are parts of congruent triangles.

 

HTH

[Stacy in NJ]

I'm going to file this one away for future reference. :001_smile:

 

 

I begin with fill in the blank proofs-- usually the statements filled in and the Reasons blank.

 

I then progress to 'mixed' blanks-- some statements and some reasons blank.

 

For a change I will mix up the statements and reasons in a proof for the student to put in order. I've found this to be a great way to teach proofs-- the student has limited options (thus more security)---and they have to think logically in order to put the proof in an acceptable order.

 

With many proofs there are numerous ways to work them correctly-- and the way one text teaches them may be completely DIFFERENT from another text! Proofs are not standard (in details) but they are standard in organization (formal proofs).

 

I worked one proof with my Geometry class today that EASILY had at least four different options (EQUALLY CORRECT) and it was only a 5 step proof!

[distancia]

Jann's idea and My3's idea both seem to make a lot of sense. My 2 cents: don't sweat it. Some math instructors are rigid about using X number of proofs but truth be told, if you get the general grasp of why and why nots, can and cannots, and the proofs/theorems themselves and how they apply, then you are doing pretty well.

 

Here's a fact that may give you some consolation: there are no proofs on the Geometry section of the SAT. None.

 

Also, a link about the same subject one year ago from the WTM: read Jann's post (#2) http://www.welltrainedmind.com/forums/archive/index.php/t-136971.html

 

My daughter's worst subject has been Geometry. When she took the SAT last year (Junior) she got 3/4 of the Geometry questions wrong--this, after a full year of Geo in public school.

 

Fast forward to this year--daughter, now homeschooled and a Senior, did a one month review, starting from page 1 of Math U See Geometry, one lesson per day. The proofs and theorems (at the end of the book, where they really should be) turned out to be a "reasoning" exercise for her. When she re-took the SATs this year she scored highest in Geometry, getting 3/4 of the questions correct.

Edited January 6, 2011 by distancia

[Tiramisu]

My daughter is using Teaching Textbooks for Geometry and understands most of the concepts and can work the problems except doing proofs. I have watched the cds for the proof explanations and I can not grasp what theorem or postulate to use either. It is not that we don't understand the theorems, postulates definitions, etc., it is when to know why you use one over the other next in the proof. Any suggestions? i am at the point of hiring a geometry tutor in our area and they are not cheap!:tongue_smilie:

 

Teaching Textbooks offers free access to a tutor. Call them and tell them you need the tutor ang give them your number. He will call you.

 

We did this last year and he was helpful and friendly.