State mathematics standards WTF

So I'm helping a friend of mine through his highschool geometry class. First, the teacher is by training a Realtor and second the state I live in is something like 48th in the union. I think I have found out why (compiled from my hideous notes from sitting in on a class):
<font size="+90">What. The. Foxtrot.</font>

Looks correct to me. Am I a cretin?
Or... wait, is the bottom half of the scan from you? What part am I supposed to be declaring wrong here?
The part labeled "STATE BENCHMARK FOR GRADE 10:" appears wrong, but I have no idea what that means...

@blakeyrat said:
Looks correct to me. Am I a cretin?
Or... wait, is the bottom half of the scan from you? What part am I supposed to be declaring wrong here?
The part labeled "STATE BENCHMARK FOR GRADE 10:" appears wrong, but I have no idea what that means...
Schools must teach by the state benchmarks. In the state benchmarks for Geometry (Grade 10) they provide that diagram, and state that within that diagram students should be able to find four (4) parallel lines.

Ok, then I get the WTF, but you really presented it in a confusing manner. I guess I can't expect much from a closet furry who loves FOSS Christmas music.

There's no WTF here. You say, in this State, the standards for grade 10 are so low that you're supposed to believe that lines that are drawn to look parallel must actually be parallel.

@Indrora said:
First, the teacher is by training a Realtor...
Hey, Realtor is a good job, compared to public school teacher. Or are you calling him an idiot because he gave up an easy career with good opportunities to make money to become a school teacher? It makes more sense that way.
@Indrora said:
...and second the state I live in is something like 48th in the union.
I'd say West Virginia, but that's probably being far too kind to WV... Nebraska?

@morbiuswilters said:
@Indrora said:
First, the teacher is by training a Realtor...
Hey, Realtor is a good job, compared to public school teacher. Or are you calling him an idiot because he gave up an easy career with good opportunities to make money to become a school teacher? It makes more sense that way.
no, this person is a realtor by trade and teacher as a secondary job (that is, she sells houses when she doesnt teach. )
@Indrora said:
...and second the state I live in is something like 48th in the union.
I'd say West Virginia, but that's probably being far too kind to WV... Nebraska?
Worse. "... So far from heaven, So close to texas" comes to mind... Its New Mexico. And it sucks balls for education.

I would have to disagree.
The following is true:
ab bc ca de
Proof:
2 lines are parallel if and only if they have equal slopes. [1]
2 lines that form 90 degree angles are perpendicular [2]
d and e both both form 90 degree angle, which since they have the same slope we can also say they are parallel. In fact ALL angles are 90 if you use the transversal rule. [1]
Lets assume for a moment that d may not have the same slope as e. Then you would have to say that the m < ad and the m < dc are NOT 90 degree angles. However, we see that they are and using the transversal rule (and a little algebra), we can say that the rest of the angles are 90 degrees.
Knowing that:
All angles are 90 degrees and that d and e are parallel one can say that a and b are also parallel due to the fact that form perpendicular lines with d and e, giving m < eb and m < ad 90 degrees. And then you can then say b and c are parallel because both are again perpendicular lines. So the initial answer is correct. Which to further prove that b and c are parallel you can say that the m < eb EQUALS m < dc which means that they will never intersect, or more simply, they have the same slope. Otherwise, in order for b and c to not be parallel then the m < eb must not equal the m < dc and thus will eventually intersect at some point.
e doesn't have to described as parallel, just as long as there is some indication that there is a difference in slope between d. Which you can see that e MUST have the same slope as d because m < ad OR m < dc EQUALS m < eb.
Which is assuming of course all of those lines are straight lines.
[1] http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut33_geom.htm
[2] http://www.terragon.com/tkobrien/algebra/topics/perpendicularlines/perpendicularlines.html
But, what do I know? I am a computer science major.

Eh, so nice of you to sign up JUST to tell us that de but I think you should try again, because there's nothing in the math that shows that those ARE parallel. They just APPEAR to be.
Prepare to defend your honor, but I sense that you're missing something fundamental in the problem definition. Like the part that there are only 3 defined 90 degree angles.

You know what they say about assumptions...
You only know that a and c are perpendicular to d and b is perpendicular to e, but how do d and e relate to each other? I'll just let that sink in and wait for your response.

@adamsna said:
I would have to disagree.
The following is true:
ab bc ca de
Proof:
2 lines are parallel if and only if they have equal slopes. [1]
2 lines that form 90 degree angles are perpendicular [2]
d and e both both form 90 degree angle, which since they have the same slope we can also say they are parallel. In fact ALL angles are 90 if you use the transversal rule. [1]
Lets assume for a moment that d may not have the same slope as e. Then you would have to say that the m < ad and the m < dc are NOT 90 degree angles. However, we see that they are and using the transversal rule (and a little algebra), we can say that the rest of the angles are 90 degrees.
Knowing that:
All angles are 90 degrees and that d and e are parallel one can say that a and b are also parallel due to the fact that form perpendicular lines with d and e, giving m < eb and m < ad 90 degrees. And then you can then say b and c are parallel because both are again perpendicular lines. So the initial answer is correct. Which to further prove that b and c are parallel you can say that the m < eb EQUALS m < dc which means that they will never intersect, or more simply, they have the same slope. Otherwise, in order for b and c to not be parallel then the m < eb must not equal the m < dc and thus will eventually intersect at some point.
e doesn't have to described as parallel, just as long as there is some indication that there is a difference in slope between d. Which you can see that e MUST have the same slope as d because m < ad OR m < dc EQUALS m < eb.
Which is assuming of course all of those lines are straight lines.
[1] http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut33_geom.htm
[2] http://www.terragon.com/tkobrien/algebra/topics/perpendicularlines/perpendicularlines.html
But, what do I know? I am a computer science major.Let me break your world.
Lets assume that m<AE=81 degrees. Your mathematics are now broken. Because it is NOWHERE STATED that ALL ANGLES ARE 90* your mathematics is now broken, as I show in the lower part of the explanation.
In geometry, In mathematics, in Life: Never. Ever. EVER. ever. ever. <font size="99">ever</font> make assumptions.

my guess its a error on the diagram.
but thats a doosy to address, marking wise.

Nonsense, the problem is expressly designed to require that people slow down and evaluate the entire situation, rather than glancing at the problem and guessing they know what is presented.
Ya know, like the way an adult should approach every problem in life. Ya know, like how we're trying to educate children by having them goto school in the first place...
Granted, the fact that the initial answerer got the question wrong implies that we've got the wrong group responsible for training our children analytical skills.

What the OP means, but states in a very confusing way, is that the diagram given the information, can just as well look like this:
(I didn't put in the text and the angles, just a quick doodle in OpenOffice Draw.

TRWTF is using "<" instead of "∠".

@RogerWilco said:
In the OP, doesn't the question state that B was parallel to both A and C?What the OP means, but states in a very confusing way, is that the diagram given the information, can just as well look like this:
(I didn't put in the text and the angles, just a quick doodle in OpenOffice Draw.
Or was that an assumption generated by (a student?) looking at the original diagram?
I thought the AB and CB was part of the question, but some of the arguments here seem to indicate it wasn't.


@PJH said:
In the OP, doesn't the question state that B was parallel to both A and C?
No, that's the claim. The erroneous claim, given the numerical information.

@Zecc said:
[explanatory image]
That's helpful.
I was confused by the fact that it's all in the same font, hiding the separation between the expected answer and the reason this answer is wrong.

@Zecc said:
[image]
Ah, right. Makes sense now.

Glad I could help.
Unless you're being ironical, in which case screw you both!
But seriously, it took me a bit to understand what was going on too.

 [URL=http://en.wikipedia.org/wiki/List_of_U.S._states_by_date_of_statehood]wiki state order[/URL] Hello new mexico, and thank you for proving how many of you are from Mexico.
 from #2 , I took one look at this and said, wtf. AC, for seperation vs appearance. But then I also attended as small, poorly (relatively) high school, and then attended a state run college. Odd, I still had a 5 on the AP Calc AB in my senior year of HS. Gee... Wonder if thats why it took me all of 2 seconds to answer the question.

@drachenstern said:
Granted, the fact that the initial answerer got the question wrong implies that we've got the wrong group responsible for training our children analytical skills.
Of course, this is obvious when you consider how many teachers would rather teach their kids how to sing praises to The One instead of teaching them the basic axioms of Euclidean geometry.

Can you please point out which one is <ae?
I didn't assume anything that is unreasonable, I used the transversal law [1] to see that many (if not all) of the angles are indeed 90 degree angles. Knowing that, you can say that the lines are perpendicular [2] because they create 90 degree angles. Which then you know that they all form right angles at some point which if they didn't they wouldn't form right angles and have different slopes. Do you want me to show how I came to this conclusion?
I pointed out some assumption test cases to attempt to show why they must be parallel.
I did assume they are straight lines, if you don't, then your math is also incorrect as if they are not straight lines then they can intersect at some point which would not make them parallel (which the definition of a parallel line includes a straight line). [3]
If you don't assume they are straight lines, then on a test that doesn't say a line is a straight line you could, in theory, put "not a straight line". I don't think the teacher would be too impressed by that though.
[1] http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut33_geom.htm
[2] http://math.about.com/od/geometry/ss/linessegments_5.htm
[3] http://en.wikipedia.org/wiki/Parallel_(geometry)

@bob171123 said:
But how do d and e relate to each other?
All I have to say to you my friend is don't quit your day job. I can't wait to see your work featured here.

Can you please point out which one is?
I tend to think "Parents". I learned more about stopping to look at the problem from my parents than I ever learned in school. Being naturally curious helps, but look what I'm doing now ... (ducks from Morb's flames)
Also, you still get the math wrong, but I think this is an elegant attempt at trolling, so I'm not responding to the remaining gibberish where it's obvious that the geometry of the problem AS DEFINED does not support your arguments. If there were merely ONE additional 90 degree marker on a single intersection not already marked, then your answer is splendid, superb and correct. And totally not necessary.

@adamsna said:
[stuff]
Could you please tell me how exactly RogerWilco's counterexample contradicts either of the only premises ∠ad=90°, ∠dc=90° or ∠eb=90°?

@bob171123 said:
@drachenstern said:
Granted, the fact that the initial answerer got the question wrong implies that we've got the wrong group responsible for training our children analytical skills.
Of course, this is obvious when you consider how many teachers would rather teach their kids how to sing praises to The One instead of teaching them the basic axioms of Euclidean geometry.
They're Matrix fans?
Adamsna: many of the angles are 90 degrees, but not enough of them to see 4 sets of parallel lines. Indoras communication skills stink, but he is right about this question. I hope he's doing the responsible thing and working on getting it fixed for next years test.

@adamsna said:
Let me break your world. Lets assume that m<AE=81 degrees. Your mathematics are now broken. Because it is NOWHERE STATED that ALL ANGLES ARE 90* your mathematics is now broken, as I show in the lower part of the explanation.
Can you please point out which one is <ae?

@adamsna said:
I didn't assume anything that is unreasonable, I used the transversal law [1] to see that many (if not all) of the angles are indeed 90 degree angles.
But what you did with this is wrong. The transversal law states that when a transverse line intersects parallel lines, corresponding angles are equal and that opposite interior angles are equal. There are several angles marked on the diagram as being right angles. But we do not have any marked angles that relate b to either a or c, so we cannot assume parallelity there. Nor do we have any data that relates d to e, so we cannot assume parallelity there.
Your only argument is that b appears to have the same slope as a and c, and that d appears to have the same slope as e. But there is nothing that allows you to make those statements with mathematical rigor. What if the slope varies by an extraordinarily small amount? Say, a factor of 10^{8}? That's well below the resolution of the displayed diagram, but it still means that those lines would eventually intersect  that they are not parallel. That's why geometry is about formal proofs and not eyeballing some figure on a test.
Using the laws of congruency for angles formed by tranverse lines intersecting parallel lines in a diagram where we cannot prove that lines are parallel is sloppy  and incorrect  geometry.

Wow, I thought this forum software could not possibly get worse then I posted from an iPhone! There was supposed to be quotes and formatting and such on that last post, but they appear to have disappeared. Oh well, the text us there.

@blakeyrat said:
@bob171123 said:
@drachenstern said:
Granted, the fact that the initial answerer got the question wrong implies that we've got the wrong group responsible for training our children analytical skills.
Of course, this is obvious when you consider how many teachers would rather teach their kids how to sing praises to The One instead of teaching them the basic axioms of Euclidean geometry.
They're Matrix fans?
The best we can hope for is that Morpheus will come along and take us away from this twisted Marxist version of reality.

@Indrora said:
<OP>
Not only is the math totally fucked, but the question is: "How many lines in the diagram left must be parallel?"
What the hell kind of sentence is that?

From the posted image, op is of course correct: a and c comprise the only provably parallel pair. But, especially since it's a reconstruction from his/her "hideous notes", I don't for minute believe it to be an accurate representation of the original question.
Clues: "highschool", disingenuousness and assumed relevance of "by training a realtor" and "the state I live in", admittedly "hideous notes", "seperate".

@Indrora said:
Worse. "... So far from heaven, So close to texas" comes to mind... Its New Mexico. And it sucks balls for education.
Sigh... It's so bad here that someone I consider of average intelligence (myself) had to be put in the advanced education program, had to skip a grade, had to transfer to another school for 6th grade as the middle schools near where I lived were terrible, and eventually had to go to a private high school.
Nobody here is really interested in education except Los Alamos.

@Storm said:
Nobody here is really interested in education except Los Alamos.
I thought Los Alamos became a part of Mexico after Davy Crockett was killed.

@morbiuswilters said:
No, no, no. Davy Crockett was a fictional character from that TV show. You're thinking of David Bowie, idiot.@Storm said:
Nobody here is really interested in education except Los Alamos.
I thought Los Alamos became a part of Mexico after Davy Crockett was killed.

@bstorer said:
No, no, no. Davy Crockett was a fictional character from that TV show. You're thinking of David Bowie, idiot.
You mean the astronaut? What does he have to do with it?
I'm pretty sure some guy named Walker was responsible.

Here's another WTF (Compiled, again from my notes in paint.NET)
My explanation is in a different font. I Think I got my math right.

@Serpentes said:
@adamsna said:
I didn't assume anything that is unreasonable, I used the transversal law [1] to see that many (if not all) of the angles are indeed 90 degree angles.
But what you did with this is wrong. The transversal law states that when a transverse line intersects parallel lines, corresponding angles are equal and that opposite interior angles are equal. There are several angles marked on the diagram as being right angles. But we do not have any marked angles that relate b to either a or c, so we cannot assume parallelity there. Nor do we have any data that relates d to e, so we cannot assume parallelity there.
Your only argument is that b appears to have the same slope as a and c, and that d appears to have the same slope as e. But there is nothing that allows you to make those statements with mathematical rigor. What if the slope varies by an extraordinarily small amount? Say, a factor of 10^{8}? That's well below the resolution of the displayed diagram, but it still means that those lines would eventually intersect  that they are not parallel. That's why geometry is about formal proofs and not eyeballing some figure on a test.
Using the laws of congruency for angles formed by tranverse lines intersecting parallel lines in a diagram where we cannot prove that lines are parallel is sloppy  and incorrect  geometry.
I do see your point. And you are correct, I was assuming those lines are parallel.
If this was a graduate class, I would agree with you and I think the professor should be smacked, however it is not. Let us propose an argument.
The OP said this was a high school class. The OP did not say what year the class was at, so since this is not an argument of mathematics, can we agree that if we assume that this was a freshman level course in math that this kind of content would be reasonable?
In the real world of mathematics, you don't assume anything  no argument there  but in a classroom you do. Teachers make mistakes lecturing, tests, and homework, which includes leaving out important information. I have even seen the wrong answers in the back of the book before. On a test in a HS classroom would you not put down 4 parallel lines? Or could you actually say that you would have the balls to put down "there are no parallel lines"? If you said the second, at that point in your HS education could you actually say you had enough knowledge to actually write out a formal proof showing that there are parallel lines? I did not. And, another argument I would like to propose is that even if you are right, it is up to the teacher to decide to give you the points or not. Even if you had a solid proof, the teacher can still mark it wrong, and I am sure we all had teachers that were like that. I personally would put down 4 parallel lines if I was in that HS class. If I was in a graduate class, I would instruct the professor that they are missing something.
That is my argument for why I "assumed" that d and e were parallel.
I am not a mathematician, but, having a programmable calculator did add to my laziness.

@adamsna said:
Or could you actually say that you would have the balls to put down "there are no parallel lines"?
Yes. Balls have nothing to do with it. It was obviously a mistake and most teachers are going to give you credit if you point it out, and the better ones will actually be pleased that you have learned well. This seems like a case of something being left off and slipping through the cracks. It's unfortunate, but I sincerely doubt that the person writing the test was so ignorant of the subject matter that he thought this was the truth.
@adamsna said:
If you said the second, at that point in your HS education could you actually say you had enough knowledge to actually write out a formal proof showing that there are parallel lines?
Yes? I went to a small, poor and mediocre high school in the rural midwest but I did formal geometry proofs my freshman year. While it's true that I was in the advanced math classes, a good 510% of my graduating class were too. And most of them would have been able to comprehend the reasoning involved, even if they may have made the same false assumption you did.

@adamsna said:
In the real world of mathematics, you don't assume anything  no argument there  but in a classroom you do. Teachers make mistakes lecturing, tests, and homework, which includes leaving out important information.No no no no NO you do not assume with mathematics, classroom or real life, especially Geometry which is so rigorously logical. Teachers can make mistakes, but the axioms upon which we base Euclidean Geometry have been right for over 2,000 years, and it's not looking like that will change any time soon. Would you trust someone who's lived 3070 years, or cold hard logic that has stood the test of time?
@adamsna said:
Or could you actually say that you would have the balls to put down "there are no parallel lines"?
No, there's obviously two parallel lines in that drawing.
@adamsna said:If you said the second, at that point in your HS education could you
actually say you had enough knowledge to actually write out a formal
proof showing that there are parallel lines?If you would use postulates do "deduce" there were four pairs of parallel lines, you certainly know enough to see the error in your reasoning.
@adamsna said:
And, another argument I would like to propose is that even if you are
right, it is up to the teacher to decide to give you the points or not.
Even if you had a solid proof, the teacher can still mark it wrong, and
I am sure we all had teachers that were like that. I personally would
put down 4 parallel lines if I was in that HS class. If I was in a
graduate class, I would instruct the professor that they are missing
something.You always have to question authority, particularly when they don't have proof or their reasoning is plain wrong. I know I did that to my HS math teachers. If you don't question it, you'll get people believing such made up statistics as "jobs saved."
@adamsna said:
I am not a mathematician, but, having a programmable calculator did add to my laziness.
I'd like to know which program you used that knew the axioms of Euclidean Geometry and could give you the correct answer to this question.

So I was feeling gutsy and asked someone who works in the state standards department. Turns out, state "Acceptable and Authorized" texbooks can have a 40% error rate. FORTY PERCENT.
At that, I've looked through the textbook and am about ready to call some serious foul on the part that: 1, the authors are not from new mexico 2, Its PrenticeHall 3, Forty Goddamn Percent Error is allowed?!?! in a MATH TEXT?!?!As for the grade, the course is designed for sophomores. In the state, the order is as follows: Algebra 1, Geometry, Algebra 2, Calculus (for an "Elective" grade if you are not a freshman this year, however you are required to take it if you're an incoming freshman).
So, see the second WTF above, gawk and go "OH MY GOD WHAT THE HELL DO THEY TEACH THESE KIDS NOW?!?!?!?!" and headdesk. Aim for a pillow, please.
As for being rewarded for finding the error? I was told to study harder and that I was wrong by the instructor. Other instructors saw the fault and went "LOL teach is an id10t." but the instructor plainly told me to my face "You are wrong. You assume that because these look parallel and the angles are 90* that they're parallel."
FUCKING HELL@adamsna said:Or could you actually say that you would have the balls to put down "there are two parallel lines"?
yes, I had the balls to write on the chapter and section tests (both included the OP diagram) that there were only two parallel lines. And what part of "GRADE 10" translates in your skull as "Freshman"? I mean seriously. In the USA, it goes middle school(6,7,8) High school (912) and on it goes.

@Indrora said:
So I was feeling gutsy and asked someone who works in the state standards department. Turns out, state "Acceptable and Authorized" texbooks can have a 40% error rate. FORTY PERCENT.
At that, I've looked through the textbook and am about ready to call some serious foul on the part that: 1, the authors are not from new mexico 2, Its PrenticeHall 3, Forty Goddamn Percent Error is allowed?!?! in a MATH TEXT?!?!To be fair, they probably don't know how much "forty percent" actually is.

@morbiuswilters said:
to be fair i think you're right.@Indrora said:
So I was feeling gutsy and asked someone who works in the state standards department. Turns out, state "Acceptable and Authorized" texbooks can have a 40% error rate. FORTY PERCENT.
At that, I've looked through the textbook and am about ready to call some serious foul on the part that: 1, the authors are not from new mexico 2, Its PrenticeHall 3, Forty Goddamn Percent Error is allowed?!?! in a MATH TEXT?!?!To be fair, they probably don't know how much "forty percent" actually is.

@Indrora said:
So, see the second WTF above, gawk and go "OH MY GOD WHAT THE HELL DO THEY TEACH THESE KIDS NOW?!?!?!?!"They teach kids to sing and dance for stimulus funds from the Messiah.

@bob171123 said:
QFT.@Indrora said:
So, see the second WTF above, gawk and go "OH MY GOD WHAT THE HELL DO THEY TEACH THESE KIDS NOW?!?!?!?!"They teach kids to sing and dance for stimulus funds from the Messiah.

@Indrora said:
@morbiuswilters said:
@Indrora said:
...and second the state I live in is something like 48th in the union.
I'd say West Virginia, but that's probably being far too kind to WV... Nebraska?
Worse. "... So far from heaven, So close to texas" comes to mind... Its New Mexico. And it sucks balls for education.
Being from New Mexico myself, I can attest to the education level being fairly low. However, you seem to be near the bottom of the barrel yourself because even I know that New Mexico was the 47th state and that Arizona was the 48th.

@morbiuswilters said:
@Indrora said:
So I was feeling gutsy and asked someone who works in the state standards department. Turns out, state "Acceptable and Authorized" texbooks can have a 40% error rate. FORTY PERCENT.
At that, I've looked through the textbook and am about ready to call some serious foul on the part that: 1, the authors are not from new mexico 2, Its PrenticeHall 3, Forty Goddamn Percent Error is allowed?!?! in a MATH TEXT?!?!To be fair, they probably don't know how much "forty percent" actually is.
It could easily be explained in terms they understand as "the approximate percentage of New Mexico vehicles that always have paper temporary license plates stuck in their back windows".

@Someone You Know said:
It could easily be explained in terms they understand as "the approximate percentage of New Mexico vehicles that always have paper temporary license plates stuck in their back windows".
"The appropriate amount to tip the coyote after he smuggles your wife across the border."
"How far we got in turning your state into a postapocalyptic, nuclear hellhole before the goddamn hippies stopped us."