How can I improve my proofs in geometry?

[Mentallic]

Geometry is arguably my weakest link in mathematics. The answers just don't "hit me" in geometry like some other sections of math do.

When trying to prove something in a polygon, such as congruence of triangles made by segments etc. I find it difficult since the equal sides/angles aren't obvious to find.

Is there any advice you can give on what needs to be looked for in certain situations? or is this question simply too absurb since the answers depend on each geometric figure?

 

[chaoseverlasting]

I think if you can imagine it somehow, see what you're looking for and then see what's available to find it. Dont know really, perhaps someone else can offer better advise than I can.

 

[dodo]

I don't know if this will be of general benefit, but I think sometimes it's useful to have a mental image of the pieces in free movement, rather that fixed.

To put a simple example, suppose you have a triangle, and the length of 2 sides is given (plus probably some other condition). It's often useful to imagine two fixed-length rods and a moving joint in the angle, and mentally play with it, see how other conditions are affected when the angle goes <90 or >90, or too small, or close to 180. I often find this "moving parts" approach more insightful that just making a drawing and staring at it. Of course, then there are cases and cases.

 

[symbolipoint]

mentallic, you are right; the relationships often do not fly out at you, which is why Geometry (Euclidean, Plane) relies on proofs. Algebra works like language, but Geometry does not work so much like that. If the course is so tough for you to study, you need two, maybe three times longer to learn it. But do not expect to learn more effectively by merely doubling or tripling the hours per week - that would be a good start, but maybe not enough for everyone. You may need to spend LONGER in terms of weeks as well.

Some people do well or enjoy Algebra 1/2 but not Geometry; some people enjoy or do well in Geometry but find Algebra 1/2 more difficult. Then, also, some people do well and enjoy the two levels of Algebra and the Geometry.

 

[Mentallic]

Some people do well or enjoy Algebra 1/2 but not Geometry;

I mainly focus my mathematics studies on algebra, because I do enjoy it and always want to learn more about it. Possibly because I'm not good at geometry could be the reason why I barely study it.
I think I need to push myself in this field of study, to expand on the proofs I know and apply them to these incognito shapes that hold proofs.

 

[chaoseverlasting]

Geometry and algebra are inter related. Once you figure that out, both fields become relatively easier.