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no angle E and it equals 180 degres
mike that's not the answer read the proof theres an e
please don't just do that I want an explanation mike.... which is why I tagged vocaloid
ah, not quite sure about this one, I would wait for the others to get here
can someone help me?
please do not ask for help on other peoples questions.... I have been waiting on this for forever and a half....
I cant help sorry. Its such a long time since I did geometry and the postulates were called different things in my time.
- also it was in the UK look like the errors are in the reasons.
yes I believe so too, but I really hope someone helps me figure this out....
what is CPCTC?
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent.
2nd repost of this question, been waiting 2 hours... wow
I've done a google on postulates of equality it looks like 7 should be the transitive postulate of equality
well that is half of it... now we just need the other error...
check this out:- http://mycoggeometric.blogspot.co.uk/2005/11/general-postulates-duducive-proofs.html what do you think?
I honestly do not know but it sounds right,
maybe also - as there are 2 sides and 1 angle involved line 8 should be SAS?
I honestly have no idea... but I hope someone actually comes to help us.....
no- SAS presumably means 2 sides and the angle in between those 2 sides
the 2 triangles are congruent by SSS because the line OE is common to both triangles
LE is congruent to NE and LO is congruent to NO
so which reasons for which steps I am confused because I am tired
I would put transitive reason for step 7 and SSS for line 8
hmmm.... alright, just food for thought though, what is your take on this perl?
The reason for number 6 is wrong
You can only use CPCTC after you show the two triangles are congruent, not before. You need a different reason
ah - that makes sense
I see, so what would te reasoning be?
I know what we used to say (lol!). If the 2 base angles of a triangle are equal then the sides opposite them are also equal ( or congruent as is said now)
What's odd about this proof, you could delete line 6 and the proof would still follow logically. Lines 1-5 and 7 are sufficient for ASA
Let me do something different. I have an idea.
it says he mae two errors though.... what are they and what should they be corrected to? and okay
The reason for 7 seems odd as well. Because thats a congruence symbol being used.
so how do we correct the two errors for the proof?
the reason for 7 could be "all right angles are congruent"
Do you have a book , i would like to check the theorems and axioms you use.
is there a property for that?
This is interesting here http://www.ohschools.k12.oh.us/userfiles/225/Classes/6019/4per2-6day3oct14.pdf
yes, but this may be asking for a property of something as the answer I am unsure.. We use properties of this and that plus definition of such and such
yes - that looks good
I'm thinking this. 6. m
There is a definition of congruent angles: If two angles have the same equal measure, then they are congruent.
yes that works thanks so much both of you!
Fred it is correct?
It is a practice worksheet that I hand into my teacher, I have to solve problems based upon what we just found which I can now do.. I will let you know later if it was correct and thanks sooooo much!
Can you see how ASA congruence follows from the previous steps:
also I don't like step 6 for another reason. You may have not learned that the sides opposite congruent base angles are congruent.
yes, it all makes sense now! 8D
iIl really have to get hold of a geometry text book for UK students and see how they teach geometry these days...
As a corollary to this proof we have OL ≅ ON by CPCTC
yes it would be nice if geometry was standardized, the way algebra is. Different books or countries sometimes use different 'reasons'.
The level of rigor that is required in a geometry proof varies.
yes I dont know what its like now but we never used the congruency symbol for angles . Just '='. Only triangles or other polygons were congruent.
yes I've seen some books dispense with congruence symbols. It looks like this proof is more detailed :)
Yes - we we never as rigorous as the US is .
The original greek euclidean proofs used congruence, not equality, for the most part.
One of the interesting things about geometry is that you can prove a lot of things without actually ever using 'numbers' .
Did they ?
You would have to add an axiom that all right angles are congruent, though.
for example you can say, the sum of the interior angles makes the same angle as a straight line.
but i might be wrong about that. I would have to ask a math historian. This is a good discussion on congruence versus equality http://mathforum.org/library/drmath/view/68400.html
There were also limitations on the use of numbers in ancient greece. They knew that there was no way to describe the diagonal of a square using ratios because it is irrational. They did not have a well developed number system like we have today.
yes that's interesting
Today we can prove all of euclid's theorem using real numbers and the coordinate plane. So called analytic geometry proofs. I don't know why we don't just do that.
No the Greeks were more or less 'all geometry' Wasn't it the arabs and hindus who invented algebra?
Yes and then descartes and fermat described geometric shapes using algebraic equation on the coordinate plane
The word algebra comes for AL Jabra which means (roughly) 'the working out'.
The history of mathematics is really interesting.
You can prove that a line intersects a circle in at most two points using analytic geometry for instance. Some proofs are easier if you use vector algebra.
In high school i was confused by the teaching of algebra 1 followed by geometry followed by algebra 2. Nobody told me the history behind these subjects.
Analytic geometry gets a boost when you include the infinitesimal world. For instance using calculus you can prove easily such things as the formula for the volume of a sphere in terms of its radius. Using synthetic geometry or euclidean methods would be difficult to prove this. Archimedes has a proof I believe.
oh ! I dont want to be rude but I've got to go . It's been an interesting conversation. My daughters calling me to take her shopping!!
Take care :)