How to do a Proof
on Wed Mar 31, 2010 10:55 pm
[08:08:28 01/04/10] hotdogsaucer : What's a proof?
[08:08:30 01/04/10] @ Tatoranaki : Please prove that this triangle is a rectangle.
[08:08:33 01/04/10] @ Tatoranaki : Using theorems.
[08:08:36 01/04/10] @ Tatoranaki : And definitions.
[08:08:40 01/04/10] @ Tatoranaki : Well... let's see.
[08:08:46 01/04/10] @ Tatoranaki : The chatbox has four sides...
[08:08:50 01/04/10] @ Tatoranaki : They're equal right?
[08:08:52 01/04/10] @ Tatoranaki : WRONG!
[08:08:54 01/04/10] @ Tatoranaki : You don't know that.
[08:09:00 01/04/10] @ Tatoranaki : You have to prove it.
[08:09:03 01/04/10] @ Tatoranaki : But how?
[08:09:10 01/04/10] @ Tatoranaki : By Theorems!
[08:09:28 01/04/10] hotdogsaucer : Ok...
[08:09:31 01/04/10] @ Tatoranaki : Lemme' find one.
[08:09:33 01/04/10] @ Tatoranaki : A proof.
[08:09:41 01/04/10] @ Tatoranaki : I'll you an example.
[08:09:49 01/04/10] hotdogsaucer : Ok
[08:09:54 01/04/10] hotdogsaucer : I'm watching
[08:09:54 01/04/10] @ Tatoranaki : Of how oh so fun they are... (voice is dripping with sarcasm)
[08:10:23 01/04/10] hotdogsaucer : ...
[08:10:31 01/04/10] @ Tatoranaki : Okay.
[08:10:35 01/04/10] @ Tatoranaki : Let's see.
[08:10:45 01/04/10] @ Tatoranaki : In every proof you have a "to prove" and a "given."
[08:10:50 01/04/10] @ Tatoranaki : The given tells you what you have.
[08:10:56 01/04/10] @ Tatoranaki : And is usually accompanied by a drawing.
[08:11:07 01/04/10] @ Tatoranaki : In a proof, it's like being in a courtroom.
[08:11:11 01/04/10] @ Tatoranaki : You must defend your case.
[08:11:25 01/04/10] @ Tatoranaki : THE CLIENT IS GUILTY!  Prosecutor
[08:11:31 01/04/10] @ Tatoranaki : Prove it.  Judge
[08:11:57 01/04/10] hotdogsaucer : ...
[08:12:10 01/04/10] @ Tatoranaki : Based on the DNA analysis taken at the scene of the crime, and the fingerprints and bullet marks, we have concluded it was Person #1. Prosecutor
[08:12:16 01/04/10] @ Tatoranaki : Very well. Judge
[08:12:32 01/04/10] @ Tatoranaki : So like a court case, you have to prove your argument.
[08:12:36 01/04/10] @ Tatoranaki : Which is the "to prove."
[08:12:42 01/04/10] hotdogsaucer : Got it
[08:13:01 01/04/10] @ Tatoranaki : Okay, one moment.
[08:13:06 01/04/10] @ Tatoranaki : Let's find a good one...
[08:13:30 01/04/10] @ Tatoranaki : One sec... lemme' dig in my horrorfilled math book.
[08:13:40 01/04/10] hotdogsaucer : Take your time
[08:14:35 01/04/10] @ Tatoranaki : Here we go!
[08:14:41 01/04/10] @ Tatoranaki : Perfect, a 5step proof.
[08:15:09 01/04/10] @ Tatoranaki : Given (which is your "evidence" that you are presented with at the beginning):
[08:15:43 01/04/10] @ Tatoranaki : Figure ABCD is a parallelogram, and M is the midpoint of segment AB.
[08:16:18 01/04/10] @ Tatoranaki : Prove (Your Case): If segment MD = MC then ABCD is a triangle.
[08:16:29 01/04/10] @ Tatoranaki : Okay, so since you can't see the picture, I'll describe it for ya'.
[08:16:38 01/04/10] @ Tatoranaki : You've got a "rectangle."
[08:16:47 01/04/10] @ Tatoranaki : With triangle in the middle.
[08:17:00 01/04/10] @ Tatoranaki : And naturally, that forms to other triangles.
[08:17:11 01/04/10] @ Tatoranaki : /\\
[08:17:17 01/04/10] @ Tatoranaki : Like that sorta'.
[08:17:18 01/04/10] hotdogsaucer : I get it
[08:17:27 01/04/10] @ Tatoranaki : I mean... /\
[08:17:28 01/04/10] @ Tatoranaki : Okay...
[08:17:31 01/04/10] @ Tatoranaki : Have you done proofs?
[08:17:36 01/04/10] hotdogsaucer : Nope
[08:17:42 01/04/10] hotdogsaucer : Is this high school stuff
[08:17:48 01/04/10] @ Tatoranaki : Ah, alright, moving on. (Yup...)
[08:17:59 01/04/10] @ Tatoranaki : Now, first we need to prove this.
[08:18:01 01/04/10] hotdogsaucer : Oh.....
[08:18:14 01/04/10] @ Tatoranaki : By presenting statements, and giving evidence for them.
[08:18:27 01/04/10] @ Tatoranaki : So every time you make a statement, you need to give a "justification."
[08:18:38 01/04/10] @ Tatoranaki : Step 1 is always presenting the given.
[08:18:48 01/04/10] @ Tatoranaki : Afterall, it's evidence that was given to you, so why not?
[08:18:51 01/04/10] @ Tatoranaki : It helps your case.
[08:19:01 01/04/10] @ Tatoranaki : So step zero looks like this.
[08:19:08 01/04/10] @ Tatoranaki : *I mean step 0, not step 1
[08:19:39 01/04/10] @ Tatoranaki : 0. ABCD is a Parallelogram, and M is the midpoint of segment AB.
[08:19:43 01/04/10] @ Tatoranaki : Then we have to prove it.
[08:19:49 01/04/10] @ Tatoranaki : 0. Given
[08:20:06 01/04/10] hotdogsaucer : Ok
[08:20:10 01/04/10] @ Tatoranaki : Next, we go onto step 1, which is where we start proving that ABCD is a rectangle.
[08:20:21 01/04/10] @ Tatoranaki : We need to prove each part, one by one.
[08:20:33 01/04/10] @ Tatoranaki : 1. Segment AM=MB
[08:20:41 01/04/10] @ Tatoranaki : Now you have various proofs and definitions.
[08:20:46 01/04/10] hotdogsaucer : ?
[08:21:06 01/04/10] @ Tatoranaki : And you must utilize your (evidence) proofs, to prove your statement.
[08:21:26] @ Tatoranaki : Here's a visual
[08:21:33] @ Tatoranaki : A_M_B
[08:21:44] @ Tatoranaki : /\
[08:21:52] @ Tatoranaki : D C
[08:21:53] hotdogsaucer : I get it!
[08:22:04] @ Tatoranaki : Yup. (combine the pictures together)
[08:22:07] hotdogsaucer : Wait, what's the DC?
[08:22:07] @ Tatoranaki : Moving on...
[08:22:17] @ Tatoranaki : The bottom.
[08:22:24] hotdogsaucer : Thanks
[08:22:26] @ Tatoranaki : Of the rectangle (and the center triangle)
[08:22:28] @ Tatoranaki : uhhuh.
[08:22:40] @ Tatoranaki : So we prove step 1 with... 1. Definition of a Midpt.
[08:22:50] hotdogsaucer : Midpt?
[08:23:20] @ Tatoranaki : Since that particular definition proves that "M" in our figure (midpoint, abbreviated) is infact a mid point.
[08:23:47] @ Tatoranaki : Step 2, we need to prove both opposite sides are equal.
[08:23:55] @ Tatoranaki : 2. AD = BC
[08:24:01] @ Tatoranaki : (prove it now...)
[08:24:25] hotdogsaucer : Keep going
[08:24:26] @ Tatoranaki : 2. Parallelograms have Opposite Sides Congruent
[08:24:42] @ Tatoranaki : (since it can also be seen as a parallelogram, by definition)
[08:25:11] hotdogsaucer : So rectangles can be called parallelograms?
[08:25:26] @ Tatoranaki : Yup.
[08:25:33] @ Tatoranaki : Since they have the same properties.
[08:25:39] @ Tatoranaki : All sides are parallel, right?
[08:25:44] @ Tatoranaki : So it's a parallelogram.
[08:25:50] hotdogsaucer : Yeah
[08:26:36] @ Tatoranaki : Just like a square is a rectangle, kite, parallelogram, trapezoid, isosceles trapezoid, kite, rhombus, and quadrilateral.
[08:26:47] @ Tatoranaki : Since it fits all those requirements.
[08:26:55] hotdogsaucer : ???
[08:27:13] hotdogsaucer : Don't squares have 4 congruent sides?
[08:27:17] @ Tatoranaki : Mhm.
[08:27:19] @ Tatoranaki : That's right.
[08:27:22] @ Tatoranaki : So it's all that.
[08:27:25] hotdogsaucer : And rectangles don't?
[08:27:30] @ Tatoranaki : Not all those are squares.
[08:27:36] @ Tatoranaki : A square is all those.
[08:27:41] @ Tatoranaki : But all those are NOT squares.
[08:27:44] @ Tatoranaki : It's a oneway thing.
[08:27:54] hotdogsaucer : Oh, I got that mixed up
[08:27:59] @ Tatoranaki : A square has everything a rectangle, trapezoid, parallelogram, etc. have.
[08:28:00] @ Tatoranaki : Mhm.
[08:28:02] hotdogsaucer : Thanks
[08:28:06] @ Tatoranaki : So next we want to prove the two triangles (opposite sides of the rectangle / \ ) are congruent.
[08:28:20] @ Tatoranaki : So, let's state that.
[08:28:42] @ Tatoranaki : 3. Triangle AMD is congruent to triangle BMC.
[08:28:48] @ Tatoranaki : Now we have to prove it...
[08:29:02] @ Tatoranaki : Which we can with SSS... which is the Side Side Side Congruence Theorem.
[08:29:42] @ Tatoranaki : And...
[08:29:51] hotdogsaucer : What's the SSS?
[08:29:54] @ Tatoranaki : The reason that is so...
[08:30:01] @ Tatoranaki : (I'm getting to that)
[08:30:14] hotdogsaucer : Sorry
[08:30:54] @ Tatoranaki : The SSS (Side Side Side Congruence Theorem) states: If, in two triangles, three sides of one are congruent to three sides of the other, then the triangles are congruent.
[08:31:29] hotdogsaucer : Thanks
[08:31:45] @ Tatoranaki : So in other words, we've been taking apart this "rectangle" (we're proving it's a rectangle), and making each part of it equal.
[08:32:25] @ Tatoranaki : Because if one part of it fails to meet the requirements, it's not a rectangle, even if it appears to be.
[08:32:35] @ Tatoranaki : Gotta prove those angles are equal.
[08:32:56] @ Tatoranaki : I mean...
[08:33:05] @ Tatoranaki : 1 sec, might as well tell you what we're trying to do...
[08:33:10] @ Tatoranaki : Prove it's a rectangle right?
[08:33:14] @ Tatoranaki : What's a rectangle?
[08:33:18] hotdogsaucer : Right
[08:33:41] hotdogsaucer : A rectangle has
[08:33:43] hotdogsaucer : 4 sides
[08:33:53] hotdogsaucer : 2 pairs of congruent sides
[08:34:24] hotdogsaucer : Right?
[08:34:51] hotdogsaucer : Or is there some other complicated way to put it?
[08:35:01] @ Tatoranaki : Always a complicated way.
[08:35:15] @ Tatoranaki : Lemme' just din it.
[08:35:24] @ Tatoranaki : *find
[08:35:36] hotdogsaucer : It's been quite complicated during this chat
[08:35:43] hotdogsaucer : ....
[08:35:49] hotdogsaucer : The chatbox is a rectangle, right?
[08:35:57] @ Tatoranaki : "A quadrilateral is a rectangle if and only if it has four right angles."
[08:35:58] hotdogsaucer : It looks like one...
[08:36:01] @ Tatoranaki : That's all it needs bud,.
[08:36:04] @ Tatoranaki : Just four right angles.
[08:36:10] hotdogsaucer : Ok
[08:36:17] @ Tatoranaki : If you prove it, then it is.
[08:36:18] hotdogsaucer : Just four right angles
[08:36:29] hotdogsaucer : Now that's some useful info
[08:36:38] @ Tatoranaki : Uhhuh, which make other things, like congruence.
[08:37:00] hotdogsaucer : Congruese is being equal in size and shape, right?
[08:37:00] @ Tatoranaki : Now this proof we're doing... has 9 steps.
[08:37:31] @ Tatoranaki : So how about I just go and finish it off, and if you get too confused, you just ask?
[08:37:48] hotdogsaucer : Sure, that'd be great
[08:38:49] hotdogsaucer : Tat?
[08:39:33] @ Tatoranaki : Typing it up.
[08:39:43] hotdogsaucer : Ok, I can wait
[08:39:50] @ Tatoranaki : 4. The Measurement of Angle A (the top lefthand edge of the rectangle) is congruent to the measurement of angle BCD (the righthand, backwards L shape of the rectangle),
[08:40:01] @ Tatoranaki : and the measurement of angle B is congruent to that of ADC.
[08:40:05] hotdogsaucer : Yes
[08:40:22] @ Tatoranaki : And the justification:
[08:40:26] hotdogsaucer : and the measurement of angle C is congruent to that of ABD?
[08:40:43] @ Tatoranaki : We're not stating that yet.
[08:40:51] @ Tatoranaki : 9 step proof. o_O
[08:40:54] hotdogsaucer : ?
[08:41:03] @ Tatoranaki : We need to state one thing at a time.
[08:41:07] @ Tatoranaki : And only if they are relative.
[08:41:12] @ Tatoranaki : *one idea
[08:41:19] hotdogsaucer : Relative?
[08:41:22] @ Tatoranaki : So to prove that...
[08:41:30] @ Tatoranaki : (make sense in other words)
[08:42:17] @ Tatoranaki : So saying triangle ABC is congruent to CBM, and segment 1 is congruent to segment 2, and the angle 3 is a right angle, makes no sense.
[08:42:33] @ Tatoranaki : Okay, so to prove step for:
[08:42:35] @ Tatoranaki : *four
[08:42:47] hotdogsaucer : Wait, then why did you state that B's angle was congruent to ACD
[08:42:56] @ Tatoranaki : 4. Parallelogram Opposite Sides are Congruent
[08:42:59] hotdogsaucer : and that A's angle was congruent to BCD?
[08:43:05] hotdogsaucer : In one step?
[08:43:06] @ Tatoranaki : (It proves the different parts of the rectangle.)
[08:43:33] @ Tatoranaki : (Then you can do transitive property, which takes two different "ideas" and "fuses" them together, in the next step.)
[08:43:43] @ Tatoranaki : Okay, here's an example:
[08:43:44] hotdogsaucer : Then why didn't you mention angle C and D's congruence?
[08:43:54] @ Tatoranaki : I'll give you an example so you'll get it.
[08:44:01] hotdogsaucer : THanks
[08:44:34] @ Tatoranaki : (this doesn't make sense in human terms, but it does in math terms)
[08:44:45] @ Tatoranaki : (just so you know, before you disagree.)
[08:44:52] hotdogsaucer : Ok
[08:44:54] @ Tatoranaki : Sally likes George.
[08:45:02] @ Tatoranaki : And George likes Mike.
[08:45:05] hotdogsaucer :
[08:45:18] @ Tatoranaki : So by the transitive property, Sally likes Mike.
[08:45:18] hotdogsaucer : NOw that's funny!
[08:45:49] @ Tatoranaki : Got it?
[08:45:51] @ Tatoranaki : XD
[08:46:08] hotdogsaucer : Wait, how does Sally like Mike if George likes Mike and Sally liking Mike wasn't previously mentioned?
[08:46:21] hotdogsaucer : And Sally likes George instead?
[08:46:34] @ Tatoranaki : Because it makes sense in math terms! lol
[08:46:52] @ Tatoranaki : This isn't a psychological exercise, and examining of human relationships.
[08:47:05] hotdogsaucer : So, they're all connected in some way?
[08:47:13] hotdogsaucer : Mathematcially
[08:47:23] @ Tatoranaki : We're saying that if Sally likes George, and George likes Mike, you can conclude that Sally likes Mike, because she likes George who likes Mike.
[08:47:31] @ Tatoranaki : Get it? Got it? Good.
[08:47:55] @ Tatoranaki : So in math terms:
[08:48:07] hotdogsaucer : Sort of like meeting a friend of a friend?
[08:48:44] @ Tatoranaki : If angle (A) is congruent to angle (B), and angle (B) is congruent to angle (C), by the transitive property, angle (A) is congruent to angle (C).
[08:48:57] @ Tatoranaki : Get it now?
[08:49:00] hotdogsaucer : Got it!
[08:49:03] hotdogsaucer :
[08:49:09] @ Tatoranaki : Haha, there we go!
[08:49:17] @ Tatoranaki : Gotcha' doing Geometry already.
[08:49:35] hotdogsaucer : What grade math is that?
[08:49:38] @ Tatoranaki : How about I post the rest of the proof with a picture on the forum later? (or tmorrow)
[08:49:45] @ Tatoranaki : 11th Grade, Sophomore.
[08:08:30 01/04/10] @ Tatoranaki : Please prove that this triangle is a rectangle.
[08:08:33 01/04/10] @ Tatoranaki : Using theorems.
[08:08:36 01/04/10] @ Tatoranaki : And definitions.
[08:08:40 01/04/10] @ Tatoranaki : Well... let's see.
[08:08:46 01/04/10] @ Tatoranaki : The chatbox has four sides...
[08:08:50 01/04/10] @ Tatoranaki : They're equal right?
[08:08:52 01/04/10] @ Tatoranaki : WRONG!
[08:08:54 01/04/10] @ Tatoranaki : You don't know that.
[08:09:00 01/04/10] @ Tatoranaki : You have to prove it.
[08:09:03 01/04/10] @ Tatoranaki : But how?
[08:09:10 01/04/10] @ Tatoranaki : By Theorems!
[08:09:28 01/04/10] hotdogsaucer : Ok...
[08:09:31 01/04/10] @ Tatoranaki : Lemme' find one.
[08:09:33 01/04/10] @ Tatoranaki : A proof.
[08:09:41 01/04/10] @ Tatoranaki : I'll you an example.
[08:09:49 01/04/10] hotdogsaucer : Ok
[08:09:54 01/04/10] hotdogsaucer : I'm watching
[08:09:54 01/04/10] @ Tatoranaki : Of how oh so fun they are... (voice is dripping with sarcasm)
[08:10:23 01/04/10] hotdogsaucer : ...
[08:10:31 01/04/10] @ Tatoranaki : Okay.
[08:10:35 01/04/10] @ Tatoranaki : Let's see.
[08:10:45 01/04/10] @ Tatoranaki : In every proof you have a "to prove" and a "given."
[08:10:50 01/04/10] @ Tatoranaki : The given tells you what you have.
[08:10:56 01/04/10] @ Tatoranaki : And is usually accompanied by a drawing.
[08:11:07 01/04/10] @ Tatoranaki : In a proof, it's like being in a courtroom.
[08:11:11 01/04/10] @ Tatoranaki : You must defend your case.
[08:11:25 01/04/10] @ Tatoranaki : THE CLIENT IS GUILTY!  Prosecutor
[08:11:31 01/04/10] @ Tatoranaki : Prove it.  Judge
[08:11:57 01/04/10] hotdogsaucer : ...
[08:12:10 01/04/10] @ Tatoranaki : Based on the DNA analysis taken at the scene of the crime, and the fingerprints and bullet marks, we have concluded it was Person #1. Prosecutor
[08:12:16 01/04/10] @ Tatoranaki : Very well. Judge
[08:12:32 01/04/10] @ Tatoranaki : So like a court case, you have to prove your argument.
[08:12:36 01/04/10] @ Tatoranaki : Which is the "to prove."
[08:12:42 01/04/10] hotdogsaucer : Got it
[08:13:01 01/04/10] @ Tatoranaki : Okay, one moment.
[08:13:06 01/04/10] @ Tatoranaki : Let's find a good one...
[08:13:30 01/04/10] @ Tatoranaki : One sec... lemme' dig in my horrorfilled math book.
[08:13:40 01/04/10] hotdogsaucer : Take your time
[08:14:35 01/04/10] @ Tatoranaki : Here we go!
[08:14:41 01/04/10] @ Tatoranaki : Perfect, a 5step proof.
[08:15:09 01/04/10] @ Tatoranaki : Given (which is your "evidence" that you are presented with at the beginning):
[08:15:43 01/04/10] @ Tatoranaki : Figure ABCD is a parallelogram, and M is the midpoint of segment AB.
[08:16:18 01/04/10] @ Tatoranaki : Prove (Your Case): If segment MD = MC then ABCD is a triangle.
[08:16:29 01/04/10] @ Tatoranaki : Okay, so since you can't see the picture, I'll describe it for ya'.
[08:16:38 01/04/10] @ Tatoranaki : You've got a "rectangle."
[08:16:47 01/04/10] @ Tatoranaki : With triangle in the middle.
[08:17:00 01/04/10] @ Tatoranaki : And naturally, that forms to other triangles.
[08:17:11 01/04/10] @ Tatoranaki : /\\
[08:17:17 01/04/10] @ Tatoranaki : Like that sorta'.
[08:17:18 01/04/10] hotdogsaucer : I get it
[08:17:27 01/04/10] @ Tatoranaki : I mean... /\
[08:17:28 01/04/10] @ Tatoranaki : Okay...
[08:17:31 01/04/10] @ Tatoranaki : Have you done proofs?
[08:17:36 01/04/10] hotdogsaucer : Nope
[08:17:42 01/04/10] hotdogsaucer : Is this high school stuff
[08:17:48 01/04/10] @ Tatoranaki : Ah, alright, moving on. (Yup...)
[08:17:59 01/04/10] @ Tatoranaki : Now, first we need to prove this.
[08:18:01 01/04/10] hotdogsaucer : Oh.....
[08:18:14 01/04/10] @ Tatoranaki : By presenting statements, and giving evidence for them.
[08:18:27 01/04/10] @ Tatoranaki : So every time you make a statement, you need to give a "justification."
[08:18:38 01/04/10] @ Tatoranaki : Step 1 is always presenting the given.
[08:18:48 01/04/10] @ Tatoranaki : Afterall, it's evidence that was given to you, so why not?
[08:18:51 01/04/10] @ Tatoranaki : It helps your case.
[08:19:01 01/04/10] @ Tatoranaki : So step zero looks like this.
[08:19:08 01/04/10] @ Tatoranaki : *I mean step 0, not step 1
[08:19:39 01/04/10] @ Tatoranaki : 0. ABCD is a Parallelogram, and M is the midpoint of segment AB.
[08:19:43 01/04/10] @ Tatoranaki : Then we have to prove it.
[08:19:49 01/04/10] @ Tatoranaki : 0. Given
[08:20:06 01/04/10] hotdogsaucer : Ok
[08:20:10 01/04/10] @ Tatoranaki : Next, we go onto step 1, which is where we start proving that ABCD is a rectangle.
[08:20:21 01/04/10] @ Tatoranaki : We need to prove each part, one by one.
[08:20:33 01/04/10] @ Tatoranaki : 1. Segment AM=MB
[08:20:41 01/04/10] @ Tatoranaki : Now you have various proofs and definitions.
[08:20:46 01/04/10] hotdogsaucer : ?
[08:21:06 01/04/10] @ Tatoranaki : And you must utilize your (evidence) proofs, to prove your statement.
[08:21:26] @ Tatoranaki : Here's a visual
[08:21:33] @ Tatoranaki : A_M_B
[08:21:44] @ Tatoranaki : /\
[08:21:52] @ Tatoranaki : D C
[08:21:53] hotdogsaucer : I get it!
[08:22:04] @ Tatoranaki : Yup. (combine the pictures together)
[08:22:07] hotdogsaucer : Wait, what's the DC?
[08:22:07] @ Tatoranaki : Moving on...
[08:22:17] @ Tatoranaki : The bottom.
[08:22:24] hotdogsaucer : Thanks
[08:22:26] @ Tatoranaki : Of the rectangle (and the center triangle)
[08:22:28] @ Tatoranaki : uhhuh.
[08:22:40] @ Tatoranaki : So we prove step 1 with... 1. Definition of a Midpt.
[08:22:50] hotdogsaucer : Midpt?
[08:23:20] @ Tatoranaki : Since that particular definition proves that "M" in our figure (midpoint, abbreviated) is infact a mid point.
[08:23:47] @ Tatoranaki : Step 2, we need to prove both opposite sides are equal.
[08:23:55] @ Tatoranaki : 2. AD = BC
[08:24:01] @ Tatoranaki : (prove it now...)
[08:24:25] hotdogsaucer : Keep going
[08:24:26] @ Tatoranaki : 2. Parallelograms have Opposite Sides Congruent
[08:24:42] @ Tatoranaki : (since it can also be seen as a parallelogram, by definition)
[08:25:11] hotdogsaucer : So rectangles can be called parallelograms?
[08:25:26] @ Tatoranaki : Yup.
[08:25:33] @ Tatoranaki : Since they have the same properties.
[08:25:39] @ Tatoranaki : All sides are parallel, right?
[08:25:44] @ Tatoranaki : So it's a parallelogram.
[08:25:50] hotdogsaucer : Yeah
[08:26:36] @ Tatoranaki : Just like a square is a rectangle, kite, parallelogram, trapezoid, isosceles trapezoid, kite, rhombus, and quadrilateral.
[08:26:47] @ Tatoranaki : Since it fits all those requirements.
[08:26:55] hotdogsaucer : ???
[08:27:13] hotdogsaucer : Don't squares have 4 congruent sides?
[08:27:17] @ Tatoranaki : Mhm.
[08:27:19] @ Tatoranaki : That's right.
[08:27:22] @ Tatoranaki : So it's all that.
[08:27:25] hotdogsaucer : And rectangles don't?
[08:27:30] @ Tatoranaki : Not all those are squares.
[08:27:36] @ Tatoranaki : A square is all those.
[08:27:41] @ Tatoranaki : But all those are NOT squares.
[08:27:44] @ Tatoranaki : It's a oneway thing.
[08:27:54] hotdogsaucer : Oh, I got that mixed up
[08:27:59] @ Tatoranaki : A square has everything a rectangle, trapezoid, parallelogram, etc. have.
[08:28:00] @ Tatoranaki : Mhm.
[08:28:02] hotdogsaucer : Thanks
[08:28:06] @ Tatoranaki : So next we want to prove the two triangles (opposite sides of the rectangle / \ ) are congruent.
[08:28:20] @ Tatoranaki : So, let's state that.
[08:28:42] @ Tatoranaki : 3. Triangle AMD is congruent to triangle BMC.
[08:28:48] @ Tatoranaki : Now we have to prove it...
[08:29:02] @ Tatoranaki : Which we can with SSS... which is the Side Side Side Congruence Theorem.
[08:29:42] @ Tatoranaki : And...
[08:29:51] hotdogsaucer : What's the SSS?
[08:29:54] @ Tatoranaki : The reason that is so...
[08:30:01] @ Tatoranaki : (I'm getting to that)
[08:30:14] hotdogsaucer : Sorry
[08:30:54] @ Tatoranaki : The SSS (Side Side Side Congruence Theorem) states: If, in two triangles, three sides of one are congruent to three sides of the other, then the triangles are congruent.
[08:31:29] hotdogsaucer : Thanks
[08:31:45] @ Tatoranaki : So in other words, we've been taking apart this "rectangle" (we're proving it's a rectangle), and making each part of it equal.
[08:32:25] @ Tatoranaki : Because if one part of it fails to meet the requirements, it's not a rectangle, even if it appears to be.
[08:32:35] @ Tatoranaki : Gotta prove those angles are equal.
[08:32:56] @ Tatoranaki : I mean...
[08:33:05] @ Tatoranaki : 1 sec, might as well tell you what we're trying to do...
[08:33:10] @ Tatoranaki : Prove it's a rectangle right?
[08:33:14] @ Tatoranaki : What's a rectangle?
[08:33:18] hotdogsaucer : Right
[08:33:41] hotdogsaucer : A rectangle has
[08:33:43] hotdogsaucer : 4 sides
[08:33:53] hotdogsaucer : 2 pairs of congruent sides
[08:34:24] hotdogsaucer : Right?
[08:34:51] hotdogsaucer : Or is there some other complicated way to put it?
[08:35:01] @ Tatoranaki : Always a complicated way.
[08:35:15] @ Tatoranaki : Lemme' just din it.
[08:35:24] @ Tatoranaki : *find
[08:35:36] hotdogsaucer : It's been quite complicated during this chat
[08:35:43] hotdogsaucer : ....
[08:35:49] hotdogsaucer : The chatbox is a rectangle, right?
[08:35:57] @ Tatoranaki : "A quadrilateral is a rectangle if and only if it has four right angles."
[08:35:58] hotdogsaucer : It looks like one...
[08:36:01] @ Tatoranaki : That's all it needs bud,.
[08:36:04] @ Tatoranaki : Just four right angles.
[08:36:10] hotdogsaucer : Ok
[08:36:17] @ Tatoranaki : If you prove it, then it is.
[08:36:18] hotdogsaucer : Just four right angles
[08:36:29] hotdogsaucer : Now that's some useful info
[08:36:38] @ Tatoranaki : Uhhuh, which make other things, like congruence.
[08:37:00] hotdogsaucer : Congruese is being equal in size and shape, right?
[08:37:00] @ Tatoranaki : Now this proof we're doing... has 9 steps.
[08:37:31] @ Tatoranaki : So how about I just go and finish it off, and if you get too confused, you just ask?
[08:37:48] hotdogsaucer : Sure, that'd be great
[08:38:49] hotdogsaucer : Tat?
[08:39:33] @ Tatoranaki : Typing it up.
[08:39:43] hotdogsaucer : Ok, I can wait
[08:39:50] @ Tatoranaki : 4. The Measurement of Angle A (the top lefthand edge of the rectangle) is congruent to the measurement of angle BCD (the righthand, backwards L shape of the rectangle),
[08:40:01] @ Tatoranaki : and the measurement of angle B is congruent to that of ADC.
[08:40:05] hotdogsaucer : Yes
[08:40:22] @ Tatoranaki : And the justification:
[08:40:26] hotdogsaucer : and the measurement of angle C is congruent to that of ABD?
[08:40:43] @ Tatoranaki : We're not stating that yet.
[08:40:51] @ Tatoranaki : 9 step proof. o_O
[08:40:54] hotdogsaucer : ?
[08:41:03] @ Tatoranaki : We need to state one thing at a time.
[08:41:07] @ Tatoranaki : And only if they are relative.
[08:41:12] @ Tatoranaki : *one idea
[08:41:19] hotdogsaucer : Relative?
[08:41:22] @ Tatoranaki : So to prove that...
[08:41:30] @ Tatoranaki : (make sense in other words)
[08:42:17] @ Tatoranaki : So saying triangle ABC is congruent to CBM, and segment 1 is congruent to segment 2, and the angle 3 is a right angle, makes no sense.
[08:42:33] @ Tatoranaki : Okay, so to prove step for:
[08:42:35] @ Tatoranaki : *four
[08:42:47] hotdogsaucer : Wait, then why did you state that B's angle was congruent to ACD
[08:42:56] @ Tatoranaki : 4. Parallelogram Opposite Sides are Congruent
[08:42:59] hotdogsaucer : and that A's angle was congruent to BCD?
[08:43:05] hotdogsaucer : In one step?
[08:43:06] @ Tatoranaki : (It proves the different parts of the rectangle.)
[08:43:33] @ Tatoranaki : (Then you can do transitive property, which takes two different "ideas" and "fuses" them together, in the next step.)
[08:43:43] @ Tatoranaki : Okay, here's an example:
[08:43:44] hotdogsaucer : Then why didn't you mention angle C and D's congruence?
[08:43:54] @ Tatoranaki : I'll give you an example so you'll get it.
[08:44:01] hotdogsaucer : THanks
[08:44:34] @ Tatoranaki : (this doesn't make sense in human terms, but it does in math terms)
[08:44:45] @ Tatoranaki : (just so you know, before you disagree.)
[08:44:52] hotdogsaucer : Ok
[08:44:54] @ Tatoranaki : Sally likes George.
[08:45:02] @ Tatoranaki : And George likes Mike.
[08:45:05] hotdogsaucer :
[08:45:18] @ Tatoranaki : So by the transitive property, Sally likes Mike.
[08:45:18] hotdogsaucer : NOw that's funny!
[08:45:49] @ Tatoranaki : Got it?
[08:45:51] @ Tatoranaki : XD
[08:46:08] hotdogsaucer : Wait, how does Sally like Mike if George likes Mike and Sally liking Mike wasn't previously mentioned?
[08:46:21] hotdogsaucer : And Sally likes George instead?
[08:46:34] @ Tatoranaki : Because it makes sense in math terms! lol
[08:46:52] @ Tatoranaki : This isn't a psychological exercise, and examining of human relationships.
[08:47:05] hotdogsaucer : So, they're all connected in some way?
[08:47:13] hotdogsaucer : Mathematcially
[08:47:23] @ Tatoranaki : We're saying that if Sally likes George, and George likes Mike, you can conclude that Sally likes Mike, because she likes George who likes Mike.
[08:47:31] @ Tatoranaki : Get it? Got it? Good.
[08:47:55] @ Tatoranaki : So in math terms:
[08:48:07] hotdogsaucer : Sort of like meeting a friend of a friend?
[08:48:44] @ Tatoranaki : If angle (A) is congruent to angle (B), and angle (B) is congruent to angle (C), by the transitive property, angle (A) is congruent to angle (C).
[08:48:57] @ Tatoranaki : Get it now?
[08:49:00] hotdogsaucer : Got it!
[08:49:03] hotdogsaucer :
[08:49:09] @ Tatoranaki : Haha, there we go!
[08:49:17] @ Tatoranaki : Gotcha' doing Geometry already.
[08:49:35] hotdogsaucer : What grade math is that?
[08:49:38] @ Tatoranaki : How about I post the rest of the proof with a picture on the forum later? (or tmorrow)
[08:49:45] @ Tatoranaki : 11th Grade, Sophomore.
Testimonials
on Wed Mar 31, 2010 11:02 pm
[09:00:27 01/04/10] hotdogsaucer : 40 minutes.......... out of my Spring Break
[09:00:33 01/04/10] hotdogsaucer : BUT
[09:00:44 01/04/10] hotdogsaucer : That was 40 minutes used wisely!
[09:00:46 01/04/10] @ Tatoranaki : (drawing...)
[09:00:49 01/04/10] @ Tatoranaki : XD
[09:00:52 01/04/10] @ Tatoranaki : Yup.
[09:00:53 01/04/10] hotdogsaucer : For I learned about proofs!
[09:00:33 01/04/10] hotdogsaucer : BUT
[09:00:44 01/04/10] hotdogsaucer : That was 40 minutes used wisely!
[09:00:46 01/04/10] @ Tatoranaki : (drawing...)
[09:00:49 01/04/10] @ Tatoranaki : XD
[09:00:52 01/04/10] @ Tatoranaki : Yup.
[09:00:53 01/04/10] hotdogsaucer : For I learned about proofs!
Re: How to do a Proof
on Fri Apr 02, 2010 9:41 pm
Awesome. And I thought you didn't like math.
Anyway, I remember doing proofs in geometry two years ago; they were really fun.
Besides SSS, the other Congruence Theorems are SAS (SideAngleSide), ASA (AngleSideAngle), AAS (AngleAngleSide) and RHS (RightangleHypotenuseSide). Very fun stuff.
Anyway, I remember doing proofs in geometry two years ago; they were really fun.
Besides SSS, the other Congruence Theorems are SAS (SideAngleSide), ASA (AngleSideAngle), AAS (AngleAngleSide) and RHS (RightangleHypotenuseSide). Very fun stuff.
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