omfg, dam geometry problem!!!!!!!! (posted solution)

Pat · **Posted:** October 17th, 2005, 4:55 pm

ok, i'm taking geometry in 8th grade

. and i'm having trouble with this problem thingy.

ok, i don't have a picture so try to imagine as best as u can:

first get a piece of paper, any sized. now fold the corners so that the sides of the corners meet the others. this should make a 90 degree or right angle. now, not only is that cool, but can anyone tell me why this is?

Adbot · **Posted:** October 17th, 2005, 4:55 pm

Chris · **Posted:** October 17th, 2005, 5:08 pm

Well, I am not sure, but I would imagine it is a theorem. Have you guys been writing down theorem regularly? That is what our class does. If you do, check those.

Pat · **Posted:** October 17th, 2005, 5:22 pm

we do, i've typed them all up and all i could fihure out is that the hypotenuses of the triangles formed are perpendicular, and idk where to go from there.

Robbie · **Posted:** October 17th, 2005, 5:32 pm

well there's 4 sides on a square, and if they all meet together, that means it's 360 degrees, and 360/4 = 90.

well at least that's what i can try and answer to that little explanation you gave

Pat · **Posted:** October 17th, 2005, 5:34 pm

they dont' all meet together, otherwise that would be a demonstration of the Pythagorean Theorem. only two of them that are on the same side of the paper.

atheism_rule · **Posted:** October 17th, 2005, 5:48 pm

hmm... i think i know...

well 1st of all, the paper has 4 right angles... when u fold two cornewrs in, it forms a pentagon with 3 rights and 2 135's
When u fold in another corner, one of the 135's gets folded in to make a right, and a flat angle(180) gets folded to make a 135 so thats still a pentagon with 2 135's and 3 rights
When u fold in the final corner, the two 135's get foleded into two rights, and that reduces a side. so now we have a square with 4 rights

Adbot · **Posted:** October 17th, 2005, 5:48 pm

Pat · **Posted:** October 17th, 2005, 6:00 pm

u can only fold 2 angles...

Pat · **Posted:** October 17th, 2005, 6:48 pm

w00000000000000000000000000t t3h 1337 r0x0rz, figured it out!!!!!!!!!!!!!!!!!!1!!!11113l3v3n!!!!!!!!!!!!!!!!one!!!!!!!11111111!!!!!!!!!

if any of u wanna know how to prove it, i'll post it here later..

Robbie · **Posted:** October 17th, 2005, 6:52 pm

what i would like, is a more detailed question.

and then the answer so i don't have to think

Chris · **Posted:** October 17th, 2005, 6:54 pm

That's nice you found it and all, but don't double post.

Pat · **Posted:** October 17th, 2005, 7:14 pm

srry, but i was 2 excited, i'm too tired to post anymore, going to sleep at 7:00 PM. lol

Evelyn · **Posted:** October 22nd, 2005, 6:06 pm

Er... Angle Addition Postulate?

Pat · **Posted:** October 23rd, 2005, 7:23 pm

no, i'll explain.

since when you fold the paper to meet, you form two right triangles.

therefore, on both of the right triangles, one angle is 90 degrees. and since the added degrees of a triangle are 180, the sum of the other two angles is 90.

So if the sum of the other two angles are 90, it makes sense that all four of them are equal to 180. Then according to the diagram:

angle1 + angle2 + angle3 + angle4 = 180.

You can get the equation: angle1 + angle2 = 90

then substitue (90 - angle3) for angle2 and you get:

angle1 + 90 - angle 3 = 90, therefore, angle1 - angle 3 = 0, which proves angle1 is congruent to angle3.

You can do the same thing to prove angle2 and angle4 congruent.
angle3 + angle4 = 90

then substitue (90 - angle2) for angle3 and you get:

angle4 + 90 - angle2 = 90, therefore, angle4 - angle2 = 0, which proves angle2 is congruent to angle4.

then you subsitute them in to the equation: angle1 + angle2 + angle3 + angle4 = 180, and get:

2angle2 + 2angle3 = 180, angle2 + angle 3 = 90. by the angle addition postulate, angle2+angle3+angleZ=180. 90+angleZ=180.

therefore, angleZ=90, which makes it a right angle.

W00t, i'm soooooooooo smart, lolz.