Help Wanted in Geometry

I face a lot of problem in solving a geometry problem. Most of the level 4 problems won't budge , let alone level 5. I have tried studying from books like Challenge and Thrill of Pre-College Mathematics and I could solve only the first few exercises of each geo. chapter. The approach to the problem doesn't strike to me, especially proving questions. Any advice, suggestion or a list of important theorems, maybe is welcome...

#Geometry #HelpMe! #Advice #Help #Suggestion

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Theorems are very important in solving geometry problems, But why don't you try to build up a theorem while solving? For example, (simple example) If one didn't know the law of cosines, he would solve a system of three equations to derive his desired answer, without knowing that he did derive a well-known theorem!

I don't mean that theorems are not important, But note that at this site, our main goal is to become more experienced and creative, so that this may lead us to create new ideas and solve unsolved problems...

My usual approach in solving geometry problems is to link all givens together, also try this:

remove one given from the question and try to solve again, you will notice at some step that something became harder, so this is a key to solve the problem, try to collect all keys and the correct time where you use them,(I always see this useful,try).

I hope I contributed in help .

Hasan Kassim - 6 years, 8 months ago

Hey, Hasan, don't mean to be a bother, but did you see the comment I wrote on one of my problems mentioning you? I thought you could help me out a bit. If you can't, that's alright. Just making sure.

Link

John M. - 6 years, 8 months ago

yes John, but I didn't yet solve both problems :|

Whenever I solve them, I will be there for you:)

The first problem ( about system of differential equations), I can not solve it bcs I am not experienced with this topic.

The second one seems challenging and I am on it :)

Hasan Kassim - 6 years, 8 months ago

@Hasan Kassim – Oh you mean the one with the badass chick in background pic? oh lol that's ok ;)

Take your time. Thank you, Hasan

John M. - 6 years, 8 months ago

Thank you, my friend..

Pankaj Joshi - 6 years, 8 months ago

Welcome :)

Hasan Kassim - 6 years, 8 months ago

@Aditya Raut @Ronak Agarwal @Calvin Lin ...

Pankaj Joshi - 6 years, 8 months ago

Actually, there is no problem in Geometry if you get it's TRICK. This trick is the part which makes a problem seemingly difficult, and if one notices that thing, then problem is easy. Talking of olympiad style problems, specially looking at the previous year RMO papers, I have always noticed that the most helpful strategy is that

$\mathbf{1.}$ Extract as much information as possible from the problem.

$\mathbf{2.}$ Think on which of the informations is going to be helpful.

$\mathbf{3.}$ People generally try proving things by high-figh theorems, but never forget to combine "Angle-chasing" with lengths. Angles many times make it easy.

$\mathbf{4.}$ Start with some of the things that you feel might help. Then, after you feel stuck at some step, start from the end, start getting things from the To Prove. Most of the times, you yourself reduce To Prove into a way simple thing and then CONNECT the approach from start with the one from end.

To know some needed (And in your words, important) theorems, the link that Shivang Jindal gives is one of the coolest....

Aditya Raut - 6 years, 8 months ago

They had taught this in the INMOTC too :P

Aditya Raut - 6 years, 8 months ago

@Aditya Raut – Thank you very much.

Pankaj Joshi - 6 years, 8 months ago

Are you aiming for math olympiads, Pankaj.

Ronak Agarwal - 6 years, 8 months ago

I am aiming only for NSEP and NSEC but I shall feel more confident if I were better at geometry. BTW, you have leveled up in many subject, I see. Any help will be appreciated..

Pankaj Joshi - 6 years, 8 months ago

@Pankaj Joshi – If you prepare for geometry having mastery in topics like co-ordinate geometry and solution of triangles will help you the most, but still question based on maths olympiads will be out of your reach.

Ronak Agarwal - 6 years, 8 months ago

@Ronak Agarwal – Where do you study geometry from?

Pankaj Joshi - 6 years, 8 months ago

Try the problems more :), i also found the book very challenging when i started , but it becomes simple, if you try hard. Give atleast an hour to the problem, you are unable to do. :)

Shivang Jindal - 6 years, 8 months ago

Yeah thanks... But thats the main problem...time... caught up with a lot of coaching work. Can you tell me where I can get the most commonly used theorems and their proofs?

Pankaj Joshi - 6 years, 8 months ago

@Pankaj Joshi – I think, for basic you don't need anything more than, Ceva's theorem , menalus theorem, power of a point, radical axis,simson lines, common triangle centres(like centroid, circumcentre, incentre,ortho,gregonne), Euler's line. Just do a google search, on these topics. Or study from here: http://www.cut-the-knot.org/Curriculum/index.shtml

Shivang Jindal - 6 years, 8 months ago

@Shivang Jindal – Thank you..

Pankaj Joshi - 6 years, 8 months ago

Not sure if my suggestions might help you.

Try learning single theorem one by one first, and then do the simple basic problems involving the theorem. After you're okay with that, try do some intermediate problems and stuffs. If you're done with more theorems, try do some geometry problems and slowly look at it, don't rush too much or trying to do it quick.

The best way to learn is to read the proofs. You can see the techniques of proving and might be able to use these for solving problems. I always do this every time when I start learning geometry.

During solving the geometry problems, try to get some information, and work with it. After some work, you might see what you need more, then you can look for them easily.

Even though I'm level 5, I still have a problem with lvl 5 problems too, because nowadays lvl 5 is freaking crazier than before.

Samuraiwarm Tsunayoshi - 6 years, 8 months ago

Thanks a lot.. I have already started trying what you suggest.

Pankaj Joshi - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$