Supertechmom Posted July 28, 2010 Share Posted July 28, 2010 who could help with this? My son needs to prove the following Given Triangle OCE is congruent to Triangle ANE Prove CA > Co He said this Triangle OCE is congruent to Triangle ANE Given CE+Eo> Co Triangle Inequality theorem EO=EA corresponding parts of congruent triangles are equal ce+ea>co substitution postulate CE+EA=CA Betweeness of Points CA>CO Substitution Postulate THE BOOK SAYS THIS (I don't have enough knowledge to argue why he's wrong or if he is right having taken a different approach) Ce+EA= CA Betweeness of points Triangle OCE is congruent to Triangle ANE Given E0=EA Corresponding parts of congruent triangles are equal CA=CE+co Substitution Postulate CE+EO > CO Triangle Inequality Theorem CA>CO Substitution Postulate The figure is hopefully attached as a zip file as I couldn't figure out any other way to load it up and I couldn't make it an image. But it is two triangles sharing line Eo pointing up between them. CE and EA are the bottom . With Triangle ANE having point N as a point on line EO . TIA! proof.zip proof.zip Quote Link to comment Share on other sites More sharing options...
Teachin'Mine Posted July 28, 2010 Share Posted July 28, 2010 :grouphug: Quote Link to comment Share on other sites More sharing options...
Supertechmom Posted July 28, 2010 Author Share Posted July 28, 2010 Thanks! :lol: It is sad when you don't have enough info to argue back. LOL! I told him I would throw his response out on the web and see if anyone with more knowledge could say he was wrong because of this and that. Otherwise, I really can't see any reason why the order and jump he did is wrong. I'm sure there probably is a wrong there but ??? I don't know. :lol: He thinks differently and we are working more toward writing the answers like the book answers to make it easier when he goes to college. Someone grading quickly isn't going to take the time to see the answer is in a different format. Quote Link to comment Share on other sites More sharing options...
Teachin'Mine Posted July 29, 2010 Share Posted July 29, 2010 You're welcome :lol: It was the best I could do. :tongue_smilie: All of the memories of having gone through the proofs just like that came flooding back. I'd have the solutions manual with the answer one way - and one way only - and dd would give me her proof. Probably perfectly fine, but since I didn't know for sure if a step was missed or a reason given not quite right, I'd have her do them over following the "thinking" used in the solutions manual. It made it the year from #%^^!!!! :svengo: It's the reason we used an outside school last year, so she could ask a math teacher when needed. It would have been awesome to have had that support for geometry. Notice how many replies you got??? :lol: Quote Link to comment Share on other sites More sharing options...
Supertechmom Posted July 29, 2010 Author Share Posted July 29, 2010 Thank YOU! We were just laughing about this. I'm going to go over again tomorrow with more coffee and chocolate and see if anything jumps out. If not, we'll call it good and roll on! LOL! (it's the first proof out of Jacob's Geometry that we have not been able to see why the answer is completely correct and ours is wrong so I am comfortable moving on) Quote Link to comment Share on other sites More sharing options...
Teachin'Mine Posted July 29, 2010 Share Posted July 29, 2010 I showed my dd the thread, and she was laughing too! :lol: Moving on sounds good!!! :) Geometry requires a lot of coffee and chocolate. Quote Link to comment Share on other sites More sharing options...
mpcTutor Posted July 29, 2010 Share Posted July 29, 2010 who could help with this? My son needs to prove the following Given Triangle OCE is congruent to Triangle ANE Prove CA > Co He said this Triangle OCE is congruent to Triangle ANE Given CE+Eo> Co Triangle Inequality theorem EO=EA corresponding parts of congruent triangles are equal ce+ea>co substitution postulate CE+EA=CA Betweeness of Points CA>CO Substitution Postulate The figure is hopefully attached as a zip file as I couldn't figure out any other way to load it up and I couldn't make it an image. But it is two triangles sharing line Eo pointing up between them. CE and EA are the bottom . With Triangle ANE having point N as a point on line EO . TIA! Your son is right and I don't see anything wrong with his proof. Although, problem asks to prove CA > CO, the zipped figure to me showed CA significantly shorter than CO without making any actual measurements. Also, triangles should appear to be congruent without actually measuring any sides or angles. So I am assuming the original diagram could be different from diagram in your attachment. Short Proof: ------------- Given: OCE & ANE as congruent triangles Consider triangle OCE, OC < CE + EO (due to triangle inequality) OC < CE + EA (due to Given, EA = EO) OC < CA (due to betweeness of points CA = CE + EA ) QED Best regards. mpcTutor www.mpclasses.com -------------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 -------------------------------------------------------------------------------- Note: If you replied to my post but didn't get an answer from me in reasonable time, I ask you to check the assumptions in your question. Thank you US Central Time: 11:30 AM 7/29/2010 Quote Link to comment Share on other sites More sharing options...
Supertechmom Posted July 29, 2010 Author Share Posted July 29, 2010 thanks! I don't know if the diagram is really accurate. they all look "off" in the book and never really seem to look they way they are supposed to. And I wasn't all the perfect on copying the figure doing that one on the fly with a baby. He's a pretty exact guy so I've had to train him to disregard the scale of the figures and assume from the given and theorems what should be equal or whatever. But thanks again. It's nice to know that the proofs can be done differently from the book in reason. He'll appreciate that! I just couldn't come up with an argument that made his proof wrong. Nice to know that it wasn't.:lol: But I still had lots of coffee and chocolate anyway! Quote Link to comment Share on other sites More sharing options...
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