# AoPS Intro to Geometry

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### #1 skimomma

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Posted 19 October 2017 - 01:47 PM

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?

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### #2 regentrude

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Posted 19 October 2017 - 02:37 PM

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, 19 October 2017 - 02:38 PM.

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### #3 skimomma

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Posted 19 October 2017 - 02:39 PM

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!

### #4 regentrude

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Posted 19 October 2017 - 02:40 PM

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, 19 October 2017 - 02:41 PM.

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Posted 19 October 2017 - 04:24 PM

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.
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### #6 TracyP

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Posted 20 October 2017 - 12:40 PM

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.

### #7 Alice

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Posted 20 October 2017 - 01:27 PM

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.

### #8 daijobu

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Posted 20 October 2017 - 05:37 PM

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.