

Geometric Theorem Help!foumy6
This is a guide of all the theorems that I can find or remember 15, so this should be a helpful resorce for you. (Credit to my Geometrey teach for handingus the lists he made :)and to myself for taking additional notes along with the for your notebook section of my text book
NOTE:You may need to shift through comments but I always post my info in red so I ask unless you are posting new information please dont post in red ) If I have any of these wrong or more you would like to add please feel free to comment. Theorems: POINTS, LINES, PLANES, AND ANGLES Theorem 11: If two lines intersect, then they intersect in exactly one point. Theorem 12: Through a line and a point not in the line, there is exactly one plane. Theorem 13: If two lines intersect, then exactly one plane contains the lines. DEDUCTIVE REASONING Theorem 21: (Midpoint Theorem) If M is the midpoint of AB, then AM =½ AB and MB =½ AB. Theorem 22: (Angle Bisector Theorem) If BX is the bisector of angle ABC, then ABX =½ ABC and XBC =½ ABC. Theorem 23: Vertical angles are congruent. Theorem 24: If two lines are perpendicular, then they form congruent adjacent angles. Theorem 25: If two lines form congruent adjacent angles, then the lines are perpendicular. Theorem 26: If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. Theorem 27: If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent. Theorem 28: If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent. PARALLEL LINES AND PLANES Theorem 31: If two parallel planes are cut by a third plane, then the lines of intersection are parallel. Theorem 32: If two parallel lines are cut by a transversal, then AIA are congruent. Theorem 33: If two parallel lines are cut by a transversal, then SSI angles are supplementary. Theorem 34: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well. Theorem 35: Two lines are cut by a transversal and the AIA are congruent, then the lines are parallel. Theorem 36: If two lines are cut by a transversal and SSI angles are supplementary then the lines are parallel. Theorem 37: In a plane two lines perpendicular to the same line are parallel. Theorem 38: Through a point outside a line, there is exactly one parallel to the given line. Theorem 39: Through a point outside a line, there is exactly one perpendicular to the given line. Theorem 310: Two lines parallel to a third line are parallel to each other. Theorem 311: The sum of the measures of the angles of a triangle is 180 degrees. C 1: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. C 2: Each angle of an equiangular triangle has a measure of 60 degrees. C 3: In a triangle, there can be at most one right angle or obtuse angle. C 4: The acute angles of a right triangle are complementary. Theorem 312: The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles. Theorem 313: The sum of the measures of the angles of a convex polygon withn sides is (n 2)180. Theorem 314: The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360 degrees. CONGRUENT TRIANGLES Theorem 41: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. C 1: An equilateral triangle is also equiangular. C 2: An equilateral triangle has three 60 degree angles. C 3: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. Theorem 42: Converse of theorem 41. Theorem 43: AAS; if two angles and a nonincluded side of one triangle are congruent to the corresponding parts of another right triangle, then they are congruent. Theorem 44: HL; if the hypotenuse and a leg on a right triangle, are congruent to that of another, then the two triangles are congruent. Theorem 45: If a point lies on the perpendicular bisector of a segment, then the point is equidistant from both ends of the segment. Theorem 46: Converse of theorem 45. Theorem 47: If a point is equidistant from the endpoints of a segment, then the point is equidistant from the sides of the angle. Theorem 48: If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle. QUADRILATERALS Theorem 51: Opposite sides of a parallelogram are congruent Theorem 52: Opposite angles of a parallelogram are congruent. Theorem 53: Diagonals of a parallelogram bisect each other. Theorem 54: If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram. Theorem 55: If one pair of opposite sides is both congruent and parallel, then the quadrilateral is a parallelogram. Theorem 56: If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram. Theorem 57: If the diagonals of a parallelogram bisect each other, then the quadrilateral is a parallelogram. Theorem 58: If two lines are parallel, then all points on one line are equidistant from the other line. Theorem 59: If three parallel lines are cut off into congruent segments on one transversal, then they cut off congruent segments in every transversal. Theorem 510: A line that contains the midpoint of one side of a triangle and is parallel to another side passes thought the midpoint of the third side. Theorem 511: The segment that joins the midpoints of two sides of a triangle (1) is parallel to the third side (2) is half as long as the third side. Theorem 512: The diagonals of a rectangle are congruent. Theorem 513: The diagonals of a rhombus are perpendicular. Theorem 514: Each diagonal of a rhombus bisects two angles of the rhombus. Theorem 515: The midpoint of the hypotenuse of aright triangle is equidistant from the three vertices. Theorem 516: If an angle of a parallelogram is a right angle, the parallelogram is a rectangle. Theorem 517: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. Theorem 518: Base angles of an isosceles trapezoid are congruent. Theorem 519: The median of a trapezoid (1) Is parallel to the bases (2) has a length equal to the average of the base lengths. sorry if this is hard to read I typed it up as fast as I could . To find more look through comments and if you have helpful things to add feel free to post tham and also please answer the poll on the page _AVG_
Wow, that is quite a comprehensive list although you did leave out Circle Theorems. And, of course, you have only provided 2dimensional theorems (but that's alright, I find 3dimensional geometry very taxing).
Perhaps, we could build this topic into a sort of Geometrical Encyclopaedia of sorts (with a list of theorems and their proofs  of course, we'll need to start off from Euclid's postulates for that). Anyway, thanks for sharing the list with us. foumy6
I have some new info to add to this and if you have more to add feel free. For this one I will be giving you some 2D geometric formulas enjoy:) MEANS ANGLE @ MEANS PI OR 3.14 ^MEANS TO THE POWER OF THE FOLLOWING NUMBER, SO 6^3 WOULD BE 6 TO THE THIRD POWER ** MEANS SQUARE ROOT * MEANS THE END OF THE RADICLE EXAMPLE: SQUARE ROOT OF THREE OVER TWO WOULD LOOK LIKE **3*/2 NOW THE SQUARE ROOT OF THREE HALVES WOULD LOOK LIKE THIS **3/2 2D SQUARE s = side Area: A = s2 Perimeter: P = 4s  RECTANGLE l = length, w = width Area: A = lw Perimeter: P = 2l + 2w  TRIANGLE b = base, h = height Area: A = 1/2bh Perimeter: P = a + b + c  EQUILATERAL TRIANGLE s = side Height: h = p**3*/2 s Area: A = p**3*/4 s^2  PARALLELOGRAM b = base, h = height, a = side Area: A = bh Perimeter: P = 2a + 2b  TRAPEZOID a, b = bases; h = height; c, d = sides Area: A = 1/2 (a + b)h Perimeter: P = a + b + c + d  CIRCLE r = radius, d = diameter Diameter: d = 2r Area: A = @r2 Circumference: C = 2@r = @d  SECTOR OF CIRCLE r = radius, = angle in radians Area: A = 1/2r^2 Arc Length: s = r  ELLIPSE a = semimajor axis b = semiminor axis Area: A = @ab Circumference: C ~ @(3(a + b)) −**(a + 3b)(b + 3a)*))  ANNULUS r = inner radius, R = outer radius Average Radius = 1/2(r + R) Width: w = R − r Area: A = @(R2− r2)  REGULAR POLYGON s = side length, n = number of sides Circumradius: R = 1/2 s csc(@/n) Area: A = 1/4ns^2 cot(@/n ) or A = 1  NEXT UPDATE: My next update which I hope to have up soon will be 3D formulas! Bikerman
Please do not simply cutpaste from other sites without:
a) Adding something of your own b) Using quote tags and citing the source. Bikerman (moderator) foumy6
:O u deleted the thing i typed up yesterday!!!!!!!!!!!!! I didnt copy and paste that I got it from my text book and notes!!!!!!!!!!!!!!!!!!!!!!!!!!!! honestley I cant bileave you did that.............. I spent an hour typeing that up and if i copied and pasted it then how would it take me an hour todo!!!!!!!!!!!! I am very upset because I came on today just to update, and now i find out im going to have to retype up everything couldn;t you have asked and not just gone ahead and deleted it????? seriously not cool! Bondings
I added the post back.
I think the confusion is due to these mathematical theorems and facts being quite similar. The information of your notes and your books is probably very similar to what is available on the internet, which caused it to look like copypaste. (And please note that a lot of people copypaste whole articles from the internet like they wrote it themselves, which is not only against the rules and annoying but can get us into trouble.) Anyway, back to geometric theorems now. Bikerman
Thanks Bondings.
foumy6  I use some software to check if postings are plagiarised (it does a pattern match using google and other sources and returns a 'hit probability'). In the case of your posting it returned a 95% probability, which is normally a surefire sign that it has been copied. I'm prepared to accept that you didn't simply copy the formulae out of the text book, but the next question is  what are you trying to achieve? These are all very standard formulae which most people here know. If you are trying to construct a resource which people can use to lookup a particular formula then this is a very bad way to do it, because it is not easily searchable. You also have the problem that the editor is not optimised for displaying formulae and it is very messy. Ideally you need a LaTeX system to display formulae correctly. It is up to you  I have no problem with you spending time typing this stuff in, but I think you would be much better advised to construct a simple database with the equations/formulae in  then it could be a useful resource which could be searched. foumy6
I assure you bikerman that this is straight from my notes, and notes my teacher prints off and hands out. It may be possible (These notes are from him) that he printed these off i don't really know. Ill ask him next chance I get, and if they were i'll ask him for the site and make sure to include that in the thread as a source anyway I hope to have my new update up tomorrow or the next day
IceCreamTruck
Honestly I've been wanting to brush up on my math. It was my favorite subject in school, and just about the only homework that I ever enjoyed doing because math has logical answers as opposed to sociology questions like "Who was the most influential person of the year 1454". I hate speculating, and then being graded on the answer I "made up" to satisfy the question.
I am curious if some of these characters might help a little bit here: http://www.zytrax.com/tech/web/entities.html
Well, I guess I got my answer because they are not translated in the forum IceCreamTruck
I suppose I could talk a little bit about AstroTwister (planet widget) that I created for yahoo widget engine here, because it is some pretty heavy math, and posed some interesting questions about robust calculations being kicked off 10 times a second or so, and how I improved it dramatically.
When I first approached the solar system widget idea my mind wanted to take it all the way up to elliptical orbits for the planets, mainly so they could go behind the sun and come back out on the other side and swing around out front, and go behind again (most apparent in mercury because it's closest to the sun). Calculating the 9 planets positions on ellipses ten times a second was crushing my computer, but the previous flat model where I constructed circular orbits for each of the planets while I was originally building the widget did not command all of the computers processing power, but the ellipses and the planets going behind each other and coming back out looked amazingly cool, so I brain stormed on the subject. My solution was to keep the circular orbits, but to shrink their height (Y values) by a percentage. This produces simulated ellipses that are just as convincing as the real thing, and keeps my widget running below 1 percent processor usage on modern computers even when it's set to full speed! Any math people out there want to explain what you call a circle that is shrunk by a percentage on the Y axis? Is that truly an ellipse, or something else completely? Here is ellipse formula: "(((xh)*(xh))/(a*a)) + (((xh)*(yk))/(a*a)) = 1" What I basically did in my widget is for every point on a circle: "(x*x) + (y*y) = (r*r)" Except I was solving for "y", so my radius was a known value: "y = SquareRoot[(r*r)  (x*x)]" I would then shrink all "y" values creating my circle by a percentage... say shrinking to 80% (y/100)*80 = 80% of "y" Yes, this can also be displayed as "y*0.8" but what fun are percentages if you don't solve for 1 percent first? Maybe that's just me. It's pretty easy on a graph if you are already graphing points of a circle... just evaluate "(y/100)*80" in each x/y coordinate for the circle. My question remains... does this satisfy the definition of an ellipse? I have never reverse engineered my equation to see if they truly form ellipses, but I can't imagine what else you would call these orbits foumy6
in this one I will show you how to add, subtract and multiple matrices. For those of you who done know what a matrices looks like i will sort of have a totorial in this post to show you what one looks like and how to read them in my guide.
 this matrix would be called a 1 by 1 matrix = [ x ] (x representing any number + or ) then you can have any soze of matrix but I'll keep it simple for now, so this would be called a 1 by 2 matrix = [ x1 x2 ] (not x to the first and x squared it is saying the first x and the secind x.  Now we get into marices having "y"s as well as x's I will start with a simple 2 by 2 matrix = x's[ x1 x2 ] (now sence there is now way for me to show you what a full matrix like this would look y's[ y1 y2 ] like I am going to just put "[ ]" again but I will label them x and y to help simplify it.)  You can get very large with matrices. Now most commonly the numbers in the martix stand for poins in a cordinate grid, but not always so if it is they will most likley have lables over each row of elements (elements are the x's and y's)like this: A B C D x's[ 3 2 4 6 ] y's[ 6 5 8 3 ] So this matrix would represent the cordinateds: A(3,6) B(2,5) C(4,8 ) D(6,3) So this whould make a qudrilateral of some sort. In my next post I will be showing you haw to add subtract, and multiply matrices. foumy6
So we will start with additon which is fairly simple lets start with a 1 by 2 matrix=
[ 2 5 ] + [ 1 8] = [ 3 13 ] For additon all you do is add the matching elements: x1 in the first matrix=2 x1 in the second matrix=1 2+1=3 then you do the same with x2's  5+8=13  Now lets get to a bit harder addition the hardest you will need to know is a 2 by 2 the rest will be easy then after: x[ 3 6 ] + [ 4 2 ] = x[ 7 8 ] y[ 2 4 ] + [ 1 6 ] = y[ 3 10] So all you do is add the x1's and x2's and the y1's and y2's  Im not going to write up a whole guide for subracting because its the same as addition just subtracting so just subtract the x1's and x2's and y1's and y2's and so on.  I 've decided to move multiplying to a different post because im out of time to work on posts todays srry IceCreamTruck
OK, you can't stop there because you have my attention... just FYI. Call it a refresher course for me because I used to know this, and it's coming back as I read your post, but I have forgotten a lot of this. x[ 3 6 ] + [ 4 2 ] = x[ 7 8 ] this equation could be for sales.... say you have 6 sales in the first three hours, and two more by the fourth hour, and you want to know how many sales per hour you have... your equation let's us keep this in grid form without breaking down and separating ideas. Just add hours to hours, and sales to sales, and you get total hours, total sales. More importantly this equation let's you do this math on the board in front of your boss instead of getting back at him when you've had time to count up all the hours and sales. Now you can just put that point on the grid and move on with your presentation. Hopefully you've had more sales than 8 in 7 hours... unless you are selling Lamborghini's. I follow, but I'm ready for the good stuff now! Your set up is good, maybe too good, but we require more meat! errr... um, math! lol foumy6
Lol I will try to get more up as soon as I can lol but for now IM Playing on the new iPad and am loving it!!!!!!! IceCreamTruck
Make sure to put frihost on your favorites list, and use the ipad to read up on your threads. Check this out too... I just sent this link to my dad: http://www.zagg.com/accessories/zaggmateipadcase I would get this keyboard if I got an ipad. I don't care for virtual keyboards. therimalaya
Taking on the Geometrical Theorems, I would like to suggest a software that can draw geometrical shapes based on geometrical principles and theorems. That is "Geogebra". This software is based on java platform. I like that software very much, it had helped me a lot in solving many problems and making different geometrical shapes and using them in different papers. Another one is "Cambri" that is also nice, but i like "Geogebra".
foumy6
Sorry I haven't been able to update in a while I have been loaded down with school work latley this is my first day where I have some time, but not enough to type up more stuff. I will as soon as I can!
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