Geometry Proofs.

  • Thread starter wubie
  • Start date
  • #1
[SOLVED] Geometry Proofs.

Hello,

I am currently taking a second year mathematics course in geometry at university. I have to do quite a few proofs and I am not used to doing proofs much less geometry proofs -last time I took geometry was when I was in grade 10 and that was over ten years ago.

So far in the course we have covered various theorems and have done proofs for these theorems. What I would like to know is, when I am attempting to prove or disprove a propostion/claim, if I state a point in my proof, can I say "by theorem"? Or once I have made a point, do I have to do a subproof and prove the theorem with respect to that point?

I hope my question is clear. Any input would be appreciated.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
43,021
970
You can certainly say "By Theorem 27" (or "14a on page 128" or cite the statement of the theorem) assuming that that theorem has already been proven. You should have shown, in previous steps, that the hypotheses of that theorem are satisfied.
 
  • #3
Hi Ivy (may I call you Ivy?),

Thanks for your reply.

In class and in the text, certain theorems have been proved and axioms are of course a given. So when I make a statement it is followed by "by Theorem ________." or "by Axiom _______."

Now what do you mean by

You should have shown, in previous steps, that the hypotheses of that theorem are satisfied.
It may seem to be an elementry statement but nothing is elementry to me.
 
  • #4
LMAO!
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,021
970
For example: a standard exercise in goemetry is to show that two angles are conguent. How you would do that, of course, depends on the exact situation. But suppose you notice that the two angles are in triangles that look suspiciously alike!

You should immediately think "Corresponding Parts of Congruent Triangles are Congruent"- since congruent triangles are precisely those that are exactly alike. Of course, just saying that they look alike isn't enough. Before you can use that, you would have to show that the triangles really are congruent.

Again, how you do that would depend on the situation. But a common way is "Side-Angle-Side": show that two sides of one triangle and the angle between them are congruent to two sides of the other triangle and the angle between them. But before you could use that you would have to show that those sides and angle are congruent. Keep going back until you get to an axiom or a "given" that you don't have to justify.

In fact, that's a common way of deciding how to prove something: work backwards. If you are to prove two segments are congruent, think of all the ways you know how to do that and look at the diagram, givens, etc. See what you have to know (what the "hypotheses" are on those theorems) and ask yourself how you would prove that. You wind up changing from "how do I prove" one thing to "how do I prove" another until, hopefully, you get to something you recognise as an axiom or given.
 
  • #6
hey, can anyone help me with this problem. I just can't concentrate hard enough to get it. Please, help me. I would really appreciate your help.
The drawing is attached in a file

Thanks.
Rahul
 

Attachments

  • help.jpg
    help.jpg
    11.3 KB · Views: 395
  • #7
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Rahul, when you have a new question it is better to start your own thread than to "hi-jack" someone elses thread!

In you picture, it appears that you intend a single line through O- a diameter. If the two "vertical" lines are not intended to be a single line, then I don't see how you can find angle y.

The marks on the lower triangle, I take it, show that the two segments are congruent. That being the case, since one of them is a radius of the circle, and the third line is a radius, you have an equilateral triangle. All angles, including the angle at the bottom are 60 degrees and angle x has measure 90- 60= 30 degrees.

Assuming I am correct about the long line through O actually being a single line: a diameter of the circle, then the large triangle is a right triangle. The angle at the bottom is 60 degrees, as said before, and the angle at the top, angle y, is 30 degrees.
 
  • #8
sorry for disturbing your conversation, but thank you for help.
I will start my own thread because I got some other problems to solve.
 
  • #9
Thanks for the advice HallsOfIvy. Those are good ideas.

Cheers.
 
  • #10
gcn_zelda
11
0
I hate proofs so much... I took Geometry in 8th grade last year, and proofs are...well...you know what I mean...
 
  • #11
Fenix
9
0
Gcn_Zelda!...

Originally posted by gcn_zelda
I hate proofs so much... I took Geometry in 8th grade last year, and proofs are...well...you know what I mean...

Well, Well, Well...

Isn't it Gcn_Zelda from the Rpgtoolkit.

Yes... we are stalking you...

Mwhahahahaha!

---------------------------

I loathe doing "proof" questions. There are really no definite answers. Instead, the majority of the answer is based on the entire structure of the steps that comes to proving. I loathe those types of questions...[zz)]

PS: 043482...
 
Last edited:
  • #12
I like proof questions


I know I'm odd :P
 

Suggested for: Geometry Proofs.

  • Last Post
Replies
4
Views
466
  • Last Post
Replies
1
Views
442
Replies
38
Views
499
Replies
1
Views
309
Replies
18
Views
356
Replies
1
Views
313
  • Last Post
Replies
2
Views
502
  • Last Post
Replies
3
Views
985
Replies
29
Views
761
  • Last Post
Replies
1
Views
537
Top