~My Geometry Therom~

[bull912000]

I was sitting in class after finishing an english test. I was doodling with three pencles in a triangle, and after sliding the bottom one up at the top of the triangle, so it was parallel to where it use to be. I then moved the two other pencles that were on the sides up and slid them to the middle so I had three lines intersecting one point. I then noticed that if the line where the first pencle use to be were still there and another line were parallel to that line (but above the first line), I would have two similar triangles. Then, I realized that if the first pencle in the middle were in the center of the two other parallel lines, it would make two congruent triangles.

 

 

 

 

 

 

 

 

 

 

 

Confusing? Ya, I thought it was. Let me clear it up:

 

 

 

 

 

 

 

 

 

 

Trying to show that these two triangles are similar

 

 

 

 

 

 

 

<1=<5 ... Alt. Int.

 

 

 

<6=<2 ... Alt. Int.

 

 

 

<3=<4 ... Vert.

 

 

 

 

 

 

 

<1=<5;

 

 

 

<6=<2;

 

 

 

<3=<4

 

 

 

 

 

 

 

Tri. 136 is similar to Tri 524... Def of Similar Tri.s

 

 

 

<=Angles

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Given that C is the midpoint of AB (and lines are parallel, I forgot to add that),

 

 

 

 

 

 

 

AC=CB ............................................ Midpoint Theorum

 

 

 

<2=<2;<3=<3 ................................ Reflexive Property

 

 

 

The Two Triangles are congruent ... ASA Theorum

 

 

 

OR...

 

 

 

 

 

 

 

The two triangles are similar...My Theorum

 

 

 

AC=BC.....................................Midpoint Theorum

 

 

 

The two triangles are similar...ASA Theorum

 

 

 

If B is the mid-point of AC, then the two triangles are congruent.

 

 

 

EDIT: Also, the two opposite interior triangles are congruent.

 

 

 

 

 

 

 

This therom states that:

 

 

 

 

 

 

 

 

 

 

Theorum X:

 

 

 

 

 

 

 

1. Any two parallel lines and any two intercecting lines that intersect withen the two parallel lines form two similar triangles.

 

 

 

 

 

 

 

and

 

 

 

2. If the intersection in the above statement is the midpoint of any two points on the parallel lines, then the triangles are congruent.

 

 

 

If anyone finds this theorum on the internet, please tell me.

[BlueLancer]

I will NEVER again claim I was bored at school, you rocked my world.

[Vito_Blade]

I will NEVER again claim I was bored at school, you rocked my world.

 

 

 

 

 

 

 

:lol:

 

 

 

 

 

 

 

Thank you for the laugh.

 

 

 

 

 

 

 

:lol:

[Mr_Putter]

Ugh...Are you for real?

[bull912000]

I can be dangerous when I'm board. Yes, I am for real. 8-)

[cyco]

I'm sorry, but I really don't get what you are trying to say. I don't see were your getting a theory from.

 

 

 

 

 

 

 

EDIT: I totally get it now. All you have to do is add the Quantum Interior Angels with the 65 and then add the outside line of Physics and then divide the 6 by the Molar Mass of the corresponding congruent angels. Yep. I have also made this diagram to help you out.

 

 

 

 

 

 

 

[bull912000]

Theorum, not theory. There's a differance.

 

 

 

 

 

 

 

This therom states that

 

 

 

 

 

 

 

1. Any two parallel lines and any two intercecting lines that intersect withen the two parallel lines form two similar triangles.

 

 

 

 

 

 

 

and

 

 

 

2. If the intersection in the above statement is the midpoint of any two points on the parallel lines, then the triangles are congruent.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EDIT AS WELL: Yup, I do aggree that the diagrams are kinda messy, but its the best I can do. As for understanding the proofs: I guess you haven't been through geometry yet, have you? You will soon if not......

[bull912000]

I just redid the post seperating the proofs and theorums with quotes. Hope it helps :D .

[godsfearme]

Remebmer it is not a theorm because it has not been tested. At best it is Posulate.

 

 

 

 

 

 

 

The whole theory is pointless becasue it is just a combination of different theorms and leads to the same conclusion because of the base theorms that made it up. A new posulate is only good if it proves what anthor theorm could not.

 

 

 

 

 

 

 

There is no counter example i can think of at this moment to prove you wrong. So for the moment you are right.

 

 

 

 

 

 

 

Therom one is the most intresting. But to know a traingle is simlar is not realy imporart in geometry.

[pro28]

There is no way you are the first to think of that; it is pretty obvious.

 

 

 

 

 

 

 

But nice find anyways, I guess.

[bull912000]

Are not all theorums just a colaboration of other theorums? There proofs, used to prove another theorum.

 

 

 

 

 

 

 

And that proof just happens to be what tested the theorum. For example, prove Vertical Angles are congruent uses angle addition postulate. Without that postulate, you would not be able to prove that statement is true.

 

 

 

 

 

 

 

In other words; in geometry, you prove theorums by other theorums, not just reword them. Even then, there have been accepted theorums that have been reworded.

 

 

 

 

 

 

 

A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. Proving theorems is a central activity of mathematicians. Note that "theorem" is distinct from "theory

[darkmage099]

Remebmer it is not a theorm because it has not been tested. At best it is Posulate.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

You're joking right? A postulate is accpeted as true. You can't just come up with a new postulate like that. It has to be a theorem because it can be proven. And so far, he's proven it.

 

 

 

 

 

 

 

I totally get what you're saying. I'm taking geometry too (9th grade)

[vmser]

That is totally trivial. Seriously.

 

 

 

 

 

 

 

You do however miss the case where the 2 'random' intersecting lines are parallel to eachother. ;) In that case you dont really get triangles...

[Bmw]

It seems like it could just be a corollary to another theorem. It's like solving a question, and in the process every step is considered a theorem :lol: Just doesn't work like that :wink:

[michiel2]

Another maths topic which I won't understand for the rest of my life.

 

 

 

:XD:

[Viktorkrum77]

Hehe, that's neat. I'm taking Trig/Pre-Calc ATM so I understand you completly.

[lawrencekill]

I understand it too. But it took a few reads for me to get it...

 

 

 

 

 

 

 

It's correct I'll give you that...

 

 

 

 

 

 

 

But I noticed one of them was like the AA similarity post.

 

 

 

 

 

 

 

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

 

 

 

 

 

 

 

So I just shot down one of your new postulate.

 

 

 

 

 

 

 

The other one is using yet another postulate and some theorems to prove your postulate.

 

 

 

 

 

 

 

The other one with midpoint. To prove they're congruent, you just have to use AAS, or some other congruence post to prove the smaller triangles then move on to the bigger ones.

 

 

 

 

 

 

 

To lazy to come up with a key.

 

 

 

 

 

 

 

Your:

 

 

 

AB=BC ............................................ Midpoint Theorum

 

 

 

<2=<2;<3=<3 ................................ Reflexive Property

 

 

 

The Two Triangles are congruent ... ASA Theorum

 

 

 

 

 

 

 

The two triangles are similar...My Theorum

 

 

 

AB=BC.....................................Midpoint Theorum

 

 

 

The two triangles are similar...ASA Theorum

 

 

 

 

 

 

 

Mine:

 

 

 

I would use the first steps same as you, then I used alt int on the midpoint line, thus proving the opposite triangles are congruent. Top left is congruent to bottom right tri, and visa versa. AAS. Then you can combine the bottom two triangles to make it congruent to top two using, ASA, SSS, AAS, or any other congruence post.

 

 

 

 

 

 

 

Ops, shot down another.

 

 

 

 

 

 

 

It's not necessarily a postulate (assumptions accepted without proof).

 

 

 

 

 

 

 

This is flawed, you can just use post or theorems to prove this without going more than 6ish steps. I'm sure there is already a theorem but I havn't finished geometry yet so I'm unsure.

 

 

 

 

 

 

 

In the future, check ALL of the theorems and postulates to see if they havn't been proven already and you're just jacking off the steps from it.

 

 

 

 

 

 

 

Very important to check, that's how some brilliant people waste their time. They spend all of it trying to prove something that's already proven (unless they're checking it), don't waste your time doing that...

 

 

 

 

 

 

 

If B is the mid-point of AC, then the two triangles are congruent.

 

 

 

EDIT: Also, the two opposite interior triangles are congruent.

 

 

 

 

 

 

 

Also it should be C is the midpoint of AB.

[Guest XplsvBam]

somebody needs calculator games,.

[cyco]

I'm sorry, but what is the point of this. I mean seriously will this make math 500x more easier for me to understand? Will this solve some huge crisis in the near future? Or is there even a point to this theorum or postulate?

[Viktorkrum77]

I'm sorry, but what is the point of this. I mean seriously will this make math 500x more easier for me to understand? Will this solve some huge crisis in the near future? Or is there even a point to this theorum or postulate?

 

 

 

 

 

 

 

The point of proofs is to provide a new way of thinking about problems. It's the thought process that counts, not the actual math and equations. Unless of course, you plan to do something involving quantum physics or some other extremely complicated area of study.

[lawrencekill]

 

I'm sorry, but what is the point of this. I mean seriously will this make math 500x more easier for me to understand? Will this solve some huge crisis in the near future? Or is there even a point to this theorum or postulate?

 

 

 

 

 

 

 

The point of proofs is to provide a new way of thinking about problems. It's the thought process that counts, not the actual math and equations. Unless of course, you plan to do something involving quantum physics or some other extremely complicated area of study.

 

 

 

 

 

 

 

It's also there to reduce steps, instead of 6 different steps, you have one theorem.

 

 

 

 

 

 

 

Oh, and thanks for the warm-up.

[bull912000]

Yes, I do admit that it is quite simple, but I take pride in finding it out miself either way.

[godsfearme]

This is just like when i thought about angle side side, dealing with a right triangle. I didn't know about the HL theorm at that time. Proably anthor theorm or posutle out their. OR else no one will accept it becasue it is just cutting steps.

[trapical]

Nice theorem. Like people said, in all honesty its not that complex, I mean if I ever came across that same picture I would be able to deduce that they were similar pretty quickly.

 

 

 

 

 

 

 

What really is cool about what you did is you first did it all without using any other theorems, you were just moving pencils. That's pretty cool :wink:

[lawrencekill]

Nice theorem. Like people said, in all honesty its not that complex, I mean if I ever came across that same picture I would be able to deduce that they were similar pretty quickly.

 

 

 

 

 

 

 

What really is cool about what you did is you first did it all without using any other theorems, you were just moving pencils. That's pretty cool :wink:

 

 

 

 

 

 

 

...Without theorems? Reread it again and again till you find out which one is a theorem, cause I KNOW that he used theorems in all of the proofs. I do not know what you have been reading.