If you want an absolutely mind-blowing proof of the centroid 2/3 proof, check out... http://www.khanacademy.org/video/triangle-medians-and-centroids--2d-proof?playlist=Geometry
... but I'm warning you, your brain may never be the same.
Turns out that this is a VERY DIFFICULT proof. We need to either do a lot of algebra (ok, so that's fun, who can argue) OR already have studied the symmetry of similar figures and paralleograms, which we have not done.
So this proof comes at an odd place in the book for me. As we have discussed, Geometry can be funny that way, some books order their theorems differently. Turns out, our prior text did not even include this as a theorem (go figure!).
BOTTOM LINE FOR YOU: You can accept this theorem without proof (I HATE THAT, but sometimes you gotta do what you gotta do) and we'll address it later in the course when we have more appropriate tools at our disposal (i.e. in our bible).
Hope this suffices for now... I will be out for the rest of the evening (yes, another math celebration... 'tis the season, you know), so I'll see you for review day tomorrow.
I'm confused on what to do for #21! I read the last part of the question and see that it has to do with overlapping triangles, but I can't find any that would help me figure out the measure!
I'm REALLY confused on the triangle folding thing on #29.. I was able to do one fold (the one pictured) but then I got lost... Could you demonstrate this in class and how it proves the Concurrency of Medians Theorem? Thanks!
Ahhh! I feel so NOT-caught up. I don't understand the method in #35 either! I can't figure out where to draw the altitude from B to... If there is no line to draw it to (I don't know where C is yet!) :S Confused!
If you want to be an architect, builder, or engineer, this knowledge is critical for your everyday work.
If you want to be an attorney, you'll want to understand these principles so you can sue negligent architects, builders, and engineers for causing an accident.
If you want to be a contributing citizen of the earth, the more know about a broad range of topics, the more interesting and valuable a person you become.
So, check out MATHCHAMBER UNIT 5 PAGE for an interesting e-lecture from the Univ of Oregon that I stumbled across. Notice also that your education is becoming increasingly electronic.
Julia, please be careful... any remaining brain matter is at risk if you click on this link!
For pg 312#6... the medians intersect at their point of concurrency, which is called the centroid. Since we know all three medians intersect at the same point, if we were to find the intersection of the first two medians, don't we already have the centroid? If we trust the theorem (we make our living trusting theorems, yes?) then all the third median will do is confirm our centroid, yes?
Okay 3 comments 1)The link for lesson quiz 5-4 on MathChamber brings you to the Unit 4 Test. I was very confused for a good 30 seconds. 2) I went onto the Lecture7 link before I read your comment about it here-totally confused. After I read your comment-less confused about why it was there, still pretty much completely confused on what it was saying 3)I went on the imaginary #s link and I don't get why a picture's dimensions are measured in imaginary #s-it's just regular dimensions. The picture's not in an alternate dimension, is it? 5) Yes I know I lied-I thought the mechanical visual with the gear and everything was a cool way to show imaginary force, but isn't that just a y variable? 6) This is the last one-that was really interesting about the i^whatever powers. How it's just a pattern...Okay I'm done
on questions 13 and 14 on the mid chapte quiz, it said the answers were 13) perpendicular bisector, angle bisector, altitude and median and 14) perpendicular bisector when i just got altitude for both.....................im confused!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
you need to know the summary of: Perp Bisectors concur at Circumcenter Angl Bisectors concur at Incenter Medians concur at Centroid Altitudes concur at Orthocenter
I'm still kind of confused on writing indirect proofs.. #19 confuses me, would we negate the "If" part of the sentence or the "Then" part of the sentence to make the first step?
Im confused on how to find the orthocenter using a set of coordinates (#15)
ReplyDeleteIf you want an absolutely mind-blowing proof of the centroid 2/3 proof, check out...
ReplyDeletehttp://www.khanacademy.org/video/triangle-medians-and-centroids--2d-proof?playlist=Geometry
... but I'm warning you, your brain may never be the same.
Turns out that this is a VERY DIFFICULT proof. We need to either do a lot of algebra (ok, so that's fun, who can argue) OR already have studied the symmetry of similar figures and paralleograms, which we have not done.
So this proof comes at an odd place in the book for me. As we have discussed, Geometry can be funny that way, some books order their theorems differently. Turns out, our prior text did not even include this as a theorem (go figure!).
BOTTOM LINE FOR YOU: You can accept this theorem without proof (I HATE THAT, but sometimes you gotta do what you gotta do) and we'll address it later in the course when we have more appropriate tools at our disposal (i.e. in our bible).
Hope this suffices for now... I will be out for the rest of the evening (yes, another math celebration... 'tis the season, you know), so I'll see you for review day tomorrow.
My questions should come soon, I hope we can review them tomorrow! :)
ReplyDeleteSorry about how late it is!
I can never explain any of the word problems!
ReplyDeleteI'm having trouble on #6. Like many other of the segments/lines, you only need two to find the ____center/centroid, but I don't know the reason why!
I'm confused on what to do for #21! I read the last part of the question and see that it has to do with overlapping triangles, but I can't find any that would help me figure out the measure!
ReplyDeleteI'm REALLY confused on the triangle folding thing on #29.. I was able to do one fold (the one pictured) but then I got lost... Could you demonstrate this in class and how it proves the Concurrency of Medians Theorem? Thanks!
ReplyDeleteOh, and #30! ^
ReplyDeleteAhhh! I feel so NOT-caught up. I don't understand the method in #35 either! I can't figure out where to draw the altitude from B to... If there is no line to draw it to (I don't know where C is yet!) :S Confused!
ReplyDeleteI just watched the Khan Academy video and I think my head is about to explode....ka-BOOM! There it went...
ReplyDeleteSounds like I'm going to make some MathChamber Academy videos this weekend... Julia, can offer you a scooper and some paper towels?
ReplyDeleteStudents often ask WHY DO WE NEED TO LEARN THIS?
ReplyDeleteIf you want to be an architect, builder, or engineer, this knowledge is critical for your everyday work.
If you want to be an attorney, you'll want to understand these principles so you can sue negligent architects, builders, and engineers for causing an accident.
If you want to be a contributing citizen of the earth, the more know about a broad range of topics, the more interesting and valuable a person you become.
So, check out MATHCHAMBER UNIT 5 PAGE for an interesting e-lecture from the Univ of Oregon that I stumbled across. Notice also that your education is becoming increasingly electronic.
Julia, please be careful... any remaining brain matter is at risk if you click on this link!
Mr. C(-bot)
oh, and btw, can you refer to a page# or worksheet# when referencing problems... thanks so much!
ReplyDeletePlease re-list any still-active questions, no need to re-state the pain and drama :)
#6
ReplyDelete#21
#29/#30
#35
My algebra class has been asking about imaginary numbers... I thought some of you might enjoy this, too...
ReplyDeletehttp://www.picomonster.com/
Be careful Julia... you might have nothing left if you click on this one!
For pg 312#6... the medians intersect at their point of concurrency, which is called the centroid. Since we know all three medians intersect at the same point, if we were to find the intersection of the first two medians, don't we already have the centroid? If we trust the theorem (we make our living trusting theorems, yes?) then all the third median will do is confirm our centroid, yes?
ReplyDeleteFor 313 #21, try this link: 5-4 pg 313-21
ReplyDeleteCan we PLEASE have the bibles for the quiz?! I have no idea how I'm going to keep track of all these altitudes and midsegments and blah blah blah!
ReplyDelete^& centers!
ReplyDeleteAnd thanks for the video, it helped!
ReplyDeleteI'm doing the mid-chapter quiz right now, I'll see if I have any questions!
No questions so far & at #17. :)
ReplyDeleteOkay 3 comments
ReplyDelete1)The link for lesson quiz 5-4 on MathChamber brings you to the Unit 4 Test. I was very confused for a good 30 seconds.
2) I went onto the Lecture7 link before I read your comment about it here-totally confused. After I read your comment-less confused about why it was there, still pretty much completely confused on what it was saying
3)I went on the imaginary #s link and I don't get why a picture's dimensions are measured in imaginary #s-it's just regular dimensions. The picture's not in an alternate dimension, is it?
5) Yes I know I lied-I thought the mechanical visual with the gear and everything was a cool way to show imaginary force, but isn't that just a y variable?
6) This is the last one-that was really interesting about the i^whatever powers. How it's just a pattern...Okay I'm done
Oops I can't count! I put 5 after 3...why did they put me in geometry again?
ReplyDeleteThat was 5 comments, Julia!
ReplyDeleteAnd Mr.C will we be able to use our bibles, I wanna know if I should start memorizing what each of the lines/segments/centers are!
Will there be any proofs on the quiz?
ReplyDeleteAnd the mid-chapter quiz went well for me, so no questions!
And will there be any paper folding on the quiz? :S Because I'm REALLY confused on that!
ReplyDeleteon questions 13 and 14 on the mid chapte quiz, it said the answers were 13) perpendicular bisector, angle bisector, altitude and median and 14) perpendicular bisector when i just got altitude for both.....................im confused!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
ReplyDeleteIf the mid-chapter quiz went well, is there anything else I should know?
ReplyDeleteMR.C! Please? :(
ReplyDeleteWill we have our bibles? Is there anything other than the mid-chapter quiz we should know?
you need to know the summary of:
ReplyDeletePerp Bisectors concur at Circumcenter
Angl Bisectors concur at Incenter
Medians concur at Centroid
Altitudes concur at Orthocenter
PAMACICO, mamcita!! Ca-peesh
No bibles... PAMACICO is all you need (and don't forget that 2/3 thing-a-ma-jig)
ReplyDeleteYAY! CA-PEESH! I'll try and study that... anything else?
ReplyDeleteApparently in Flores math, 4 is an imaginary number?
ReplyDeleteI can't memorize all these theorems :(
ReplyDeleteYeah, the symbol for 4 is invisible, just like those parentheses we used to talk about in good old algebra :)
ReplyDeleteI'm still kind of confused on writing indirect proofs.. #19 confuses me, would we negate the "If" part of the sentence or the "Then" part of the sentence to make the first step?
ReplyDelete