WILL MEDAL AND FAN! HELP BEEN WAITING FOREVVVERRRRR! Find the two errors in this two-column proof and correct them.

- FredFredBurgerYes

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- FredFredBurgerYes

##### 1 Attachment

- FredFredBurgerYes

@Vocaloid @Preetha @welshfella

- anonymous

no angle E
and it equals 180 degres

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## More answers

- FredFredBurgerYes

mike that's not the answer read the proof theres an e

- anonymous

step 7

- FredFredBurgerYes

please don't just do that I want an explanation mike.... which is why I tagged vocaloid

- Vocaloid

ah, not quite sure about this one, I would wait for the others to get here

- FredFredBurgerYes

@skullpatrol

- anonymous

can someone help me?

- FredFredBurgerYes

please do not ask for help on other peoples questions.... I have been waiting on this for forever and a half....

- welshfella

I cant help sorry. Its such a long time since I did geometry and the postulates were called different things in my time.

- FredFredBurgerYes

:(

- FredFredBurgerYes

@uri @pooja195 @ganeshie8 helppp

- FredFredBurgerYes

@Miracrown @karatechopper help please!

- FredFredBurgerYes

@Abhisar help!!!!

- welshfella

- also it was in the UK
look like the errors are in the reasons.

- FredFredBurgerYes

yes I believe so too, but I really hope someone helps me figure this out....

- welshfella

what is CPCTC?

- FredFredBurgerYes

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.

- FredFredBurgerYes

2nd repost of this question, been waiting 2 hours... wow

- FredFredBurgerYes

@paki @kropot72 @Luigi0210 @sleepyjess

- welshfella

I've done a google on postulates of equality
it looks like 7 should be the transitive postulate of equality

- FredFredBurgerYes

well that is half of it... now we just need the other error...

- welshfella

check this out:-
http://mycoggeometric.blogspot.co.uk/2005/11/general-postulates-duducive-proofs.html
what do you think?

- FredFredBurgerYes

I honestly do not know but it sounds right,

- welshfella

maybe also - as there are 2 sides and 1 angle involved line 8 should be SAS?

- FredFredBurgerYes

@dan815 @nincompoop @Preetha @ganeshie8 @texaschic101 @Data_LG2 @jagr2713 @acxbox22 @Mimi_x3 @YanaSidlinskiy PLEASE HELPPPPP

- FredFredBurgerYes

I honestly have no idea... but I hope someone actually comes to help us.....

- welshfella

no- SAS presumably means 2 sides and the angle in between those 2 sides

- FredFredBurgerYes

@perl some assistance please?

- welshfella

|dw:1435172128577:dw|

- FredFredBurgerYes

@perl

- welshfella

the 2 triangles are congruent by SSS because the line OE is common to both triangles

- welshfella

LE is congruent to NE and LO is congruent to NO

- FredFredBurgerYes

so which reasons for which steps I am confused because I am tired

- welshfella

I would put transitive reason for step 7 and SSS for line 8

- FredFredBurgerYes

hmmm.... alright, just food for thought though, what is your take on this perl?

- perl

The reason for number 6 is wrong

- perl

You can only use CPCTC after you show the two triangles are congruent, not before.
You need a different reason

- welshfella

ah - that makes sense

- FredFredBurgerYes

I see, so what would te reasoning be?

- welshfella

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)

- perl

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

- perl

Let me do something different. I have an idea.

- FredFredBurgerYes

it says he mae two errors though.... what are they and what should they be corrected to? and okay

- welshfella

is transitive equality correct @perl

- perl

The reason for 7 seems odd as well. Because thats a congruence symbol being used.

- FredFredBurgerYes

so how do we correct the two errors for the proof?

- perl

the reason for 7 could be
"all right angles are congruent"

- perl

Do you have a book , i would like to check the theorems and axioms you use.

- FredFredBurgerYes

is there a property for that?

- perl

This is interesting here
http://www.ohschools.k12.oh.us/userfiles/225/Classes/6019/4per2-6day3oct14.pdf

- FredFredBurgerYes

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

- welshfella

yes - that looks good

- perl

I'm thinking this.
6. m

- perl

There is a definition of congruent angles:
If two angles have the same equal measure, then they are congruent.

- FredFredBurgerYes

yes that works thanks so much both of you!

- welshfella

yw

- perl

Fred it is correct?

- perl

|dw:1435184442325:dw|

- FredFredBurgerYes

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!

- perl

Can you see how ASA congruence follows from the previous steps:

- perl

also I don't like step 6 for another reason.
You may have not learned that the sides opposite congruent base angles are congruent.

- FredFredBurgerYes

yes, it all makes sense now! 8D

- welshfella

iIl really have to get hold of a geometry text book for UK students and see how they teach geometry these days...

- perl

As a corollary to this proof we have OL ≅ ON by CPCTC

- perl

yes it would be nice if geometry was standardized, the way algebra is. Different books or countries sometimes use different 'reasons'.

- perl

The level of rigor that is required in a geometry proof varies.

- welshfella

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.

- perl

yes I've seen some books dispense with congruence symbols. It looks like this proof is more detailed :)

- welshfella

Yes - we we never as rigorous as the US is .

- perl

The original greek euclidean proofs used congruence, not equality, for the most part.

- perl

One of the interesting things about geometry is that you can prove a lot of things without actually ever using 'numbers' .

- perl

or measures

- welshfella

Did they ?

- perl

You would have to add an axiom that all right angles are congruent, though.

- welshfella

yes

- perl

for example you can say, the sum of the interior angles makes the same angle as a straight line.

- welshfella

yes

- perl

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

- perl

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.

- welshfella

yes that's interesting

- perl

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.

- welshfella

No the Greeks were more or less 'all geometry'
Wasn't it the arabs and hindus who invented algebra?

- perl

Yes and then descartes and fermat described geometric shapes using algebraic equation on the coordinate plane

- welshfella

The word algebra comes for AL Jabra which means (roughly) 'the working out'.

- welshfella

The history of mathematics is really interesting.

- perl

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.

- perl

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.

- perl

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.

- welshfella

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!!

- perl

Take care :)

- welshfella

ty bye

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