Question Bank Geometry #2 "Splitting Triangle"

[yannickdago]

Hi MGMAT team,

Please see below the "Splitting Triangle" problem from the Geometry Question Bank :

In triangle ABC to the right, if BC = 3 and AC = 4, then what is the length of segment CD?

(A) 3 (B) 15/4 (C) 5 (D) 16/3 (E) 20/3

The correction states that « Any time a height is dropped from the right angle vertex of a right triangle to the opposite side of that right triangle, the three resulting triangles have the same 3 angle measures. »
Can you please indicate on which page of the geometry strategy guide (or any other MGMAT study material) is this property addressed (I could not find it) ?
Also, which "3 angles" are we talking about ?

Thanks for your feedback

Yannick

[RonPurewal]

Well, it's not really possible to reply directly to your post, since a picture of the triangle is not included. (If necessary, you can upload the image to postimage.org and then post the link here.)

This page may help:
http://www.cliffsnotes.com/math/geometr ... hypotenuse

[yannickdago]

Thank you.
It makes more sense now.
For future postings, can you elaborate on how to use postimage.org ?
Also, is it possible to attach Word pages to questions in the forum ?

Yannick

[yannickdago]

Hi Ron,

On another subject, how can we know in advance topics that will be addressed during Thursday's Study hall sessions ?

Thanks for your feedback

Yannick

[RonPurewal]

Hi Ron,

On another subject, how can we know in advance topics that will be addressed during Thursday's Study hall sessions ?

Thanks for your feedback

Yannick

I don't even make that decision until about an hour before the session. So, you can't.

The only exception is sessions that have a lot of questions left over at the end, because we spend longer on them than I'd anticipated. In that case, you can expect a continuation of the topic from the previous session. (When that happens, I'll usually say something near the end -- "we've got more of this for next time", or something along those lines.)

[vak3e]

Bonjour Ron, j'ai une question pour vous...

J'ai toujours des difficultés avec les triangles similaires. Whoops, wrong language...haha

Ok, so I always find it difficult to go about figuring out what side is similar to what side. I mean in this particular problem it took me like 5 minutes just to figure this out by rotating the triangles in my head and scribbling stuff. (and I'm not weak in Quant.) Just wondering, is there a particular mental checklist that you go through while doing triangle similarity problems?

I'm sorry but I can't attach the image to this problem either, not sure how this Img thing work. Thank you!!!

[RonPurewal]

I'd need to see the picture to say for sure.

If the problem involves right triangles, just draw a right triangle with vastly different leg lengths (i.e., a right triangle with angles of 10-20º and 70-80º"”i.e., NOT anything approximating a 45º-45º-90º triangle). That way, when you split up the triangle, it should be pretty clear which sides correspond to each other.

[RonPurewal]

Just wondering, is there a particular mental checklist that you go through while doing triangle similarity problems?

You'll be a better problem solver if you don't have a "mental checklist". Any sort of "checklist" will impede mental flexibility.

"Mental checklists" can help you avoid things like leaving the door unlocked when you leave home, but they aren't going to help you solve unusual problems. Quite the opposite, really.

I'm sorry but I can't attach the image to this problem either, not sure how this Img thing work. Thank you!!!

You can always just upload it to an image hosting site, and then post the link here.

[vak3e]

Just to clarify, by mental checklist I mean a "common approach" to start off a particular type of problem. For example, for DS qs, I started "mentally check-listing" that I'm certain what type of numbers are refered to (integer, non-zero, etc.) This significantly helped.

Also, I was playing around with the triangle, (and like you said, it was similar to 45 45 degree in the diagram), and redrawing it definitely helped so that would be a good "checklist approach" whenever there's a q about triangle similarity and it's hard to see what the sides are similar too.

Also, when doing DS in general, it's really helped me a lot to go about each point in a highly systemized way.

That's the sort of thing I meant, I hope you'd agree that's a good way to go about solving these problems, if you have any other comments about that I'd really appreciate it :)

Thank you!

[RonPurewal]

In a very general sense, I'd say something like this:
"- Read through the problem statement slowly and carefully. Do not rush through the problem statement.
"- Note what kind of information is in the problem.
"- See whether any associations come to mind. Do the given concepts remind you of any other concepts? Do any particular equations/rules/techniques come to mind? Is there anything you could organize into a chart or diagram? Etc.

Basically, you should try to get your mental gears turning before you start doing "scratch work" or actual mathematics. That way, you'll actually have goals, even if they might be vague at first.
If you just jump right into scrawling down random work as soon as you've read one line, it's too easy to get lost (or to start out already lost).

[griffin.811]

http://postimg.org/image/tuaw9d5dz/

Hi Ron, the question, and associated pic are at the link above.

My question revolves around the idea of this problem creating three similar triangles (as a height is dropped from a right angle).

I can clearly see where each triangle's right angle, and hypotenuse are, but how do you know which sides on each triangle are pairs?

For instance, if I leave the original triangle as is (ADB, when naming clockwise), line BD is the hypotenuse. However, when I go to pair that with smaller triangle ABC, I cannot determine the placement of angles B and A (I know that C would be on the top). Going clockwise, and starting from the top, would the triangle be CBA, or CAB? I also have the same issue with the other smaller triangle. Should that be CAD, or CDA?

Usually I'd anchor the right angle, and the smallest angle and fill in from there, but with this question, there doesn't seem to be enough info to do this.

Thanks for your help!

[RonPurewal]

This should be covered here:
post105113.html

[griffin.811]

Found it, good explanations.

I think the question number has changed though. It's now question 2 in the question bank.

Thanks!

[RonPurewal]

Found it, good explanations.

I think the question number has changed though. It's now question 2 in the question bank.

Thanks!

That's possible.

Incidentally, this is also why the forum rules are what they are, in regard to the correct way to title threads (= the first few words of the problem).
If a thread is titled according to the first few words of the problem, then a change in problem # becomes irrelevant.