Menu
Jump to content

What's with the ads?

skimomma

AoPS Intro to Geometry

Recommended Posts

This is for anyone who is currently working or has recently worked through this book.

 

Dd has been loving Intro to Geometry.  She also was very challenged by but also enjoyed Pre-A and Intro to A.  As I have mentioned on here a few times, this program is a funny fit for my not-terribly-mathy dd but she likes the approach so we have stuck with it.

 

She is currently working through Chapter 5 (Similar Triangles).  I am also working through the book and am a section or two ahead just so I can help when she needs it.  Dd is just starting to have trouble and as I work a little ahead, I am finding the exercises to be very difficult, even though geometry was my favorite math class and I have taken years and years of advanced math.  I can solve them but can see that dd is struggling to puzzle together the path for the more complicated problems despite being pretty rock-solid on the concepts.  I am finding I have to help a lot.  The next chapter is Right Triangles.  Anyone happen to know or remember if the Similar Triangles chapter was particularly difficult or are we in for a rough ride the rest of the year?

  • Like 1

Share this post


Link to post
Share on other sites

I have gone through the book with two different students and do not recall this chapter as more difficult than others.

But it was definitely puzzle like, and some problems just took a looong time. I recall one proof taking me two hours, even the second time around, but I don't remember whether it was in this chapter.

You may already been doing this: I made my students draw a figure for every problem, and had them use colored pencils to draw corresponding parts in same colors - that helped tremendously.

Edited by regentrude
  • Like 1

Share this post


Link to post
Share on other sites

I have gone through the book with two different students and do not recall this chapter as more difficult than others.

But it was definitely puzzle like. 

You may already been doing this: I made my students draw a figure for every problem, and had them use colored pencils to draw corresponding parts in same colors - that helped tremendously.

 

I do make her create a drawing, no matter what, but no colors.  That is a great idea!  Thanks!

Share this post


Link to post
Share on other sites

I do make her create a drawing, no matter what, but no colors.  That is a great idea!  Thanks!

 

I really found colors also helped me to work through the difficult problems. I am not a visual person, and despite years of advanced math (I am a theoretical physicist) struggle with visualization. AoPS Geo definitely challenged me.

Edited by regentrude

Share this post


Link to post
Share on other sites

I wouldn't say so. We found three dimensional geometry and some sections of analytic geometry very difficult. Similar triangles chapter was on the easier side for us.

  • Like 1

Share this post


Link to post
Share on other sites

I didn't find that chapter very difficult, but my dd struggled with it. I can't remember the details. I just know that is where I almost switched programs. We were fine after that until we hit the 3D chapters; we got completely bogged down there and had to supplement with a different program.

Share this post


Link to post
Share on other sites

We’re on the same chapter. I love the colors idea, I’ll have to tell that to ds. One thing that has helped him has been for me to show him how to start thinking about a proof backwards. Sometimes he doesn’t even know where to start and just is stuck. So I showed him how to start with what you want to prove, then think about what do I need to prove that and work backwards until you can figure out how to work forwards.

Share this post


Link to post
Share on other sites

When comparing similar triangles, I find it helpful to redraw the triangles separately with corresponding sides oriented the same way and congruent angles clearly marked and vertices labeled.  Then you can work your way through the ratios.  

 

I thought the toughest chapter was chapter 7, covering the different "centers": orthocenter, incenter, circumcenter, and centroid.  Before you begin each section, review what you've already learned and be able to do a quick back of the envelope derivation of all the centers you've learned so far.

 

You should be able to reason: since points on the angle bisectors are equally distant from each side, the intersection of the 3 angle bisectors should be the incenter since this point is equally distant from all 3 sides.   

Share this post


Link to post
Share on other sites

Coloring angles and sometimes sides has helped us a lot in chps 3 & 4.

 

We took an hour to work through two ch 4 review challenge problems today. Yesterday was also an hour for 2 problems.

Edited by Sebastian (a lady)

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

SUBSCRIBE TO OUR NEWSLETTER & RECEIVE A COUPON FOR
10% OFF
We respect your privacy.You’ll hear about new products, special discounts & sales, and homeschooling tips. *Coupon only valid for first-time registrants. Coupon cannot be combined with any other offer. Entering your email address makes you eligible to receive future promotional emails.
0 Shares
Share
Tweet
Pin
×