This Blog exists for the collective benefit of all geometry students. While the posts are specific to Mr. Chamberlain's class, any and all "geometricians" are welcome. The more specific your question (including your own attempts to answer it) the better.
on number 18 page 108 when it says the angles opposite does it mean the supplementary angles?
same thing on number 19 what does the book mean by opposite?
on number 26b (page 108) it says write a deductive proof. What's a deductive proof?
on number 29 page 109 what's the number of diagonals (like what does it mean not what's the answer)? is that the number of auxiliary lines we can draw in a polygon to make triangles?
on page 109 number 30 i have no idea how to even get started with trying to figure out the measure of the angles.
and i just want to get one thing clear. okay so the sum of the exterior angles are always 360 no matter how many sides right?
i'm not sure about number 4 on the chapter review on page 111 i want to say no but i'm not entirely sure the r and s could be parallel and j could skew r and intersect with s and s and r would still be parallel
for 15 on page 111 i can say angle 2 is congruent to angle 8 but i dont know what the reason is
and that's all that i can find. i only read the problems i didnt do any yet so if i find any i'll blog it
But that would be horrible! Have you not learned anything? By inductive reasoning, whenever we aren't miserable, Mr.C gets mad. From here we would assume that if we do well on the test he will be mad. You don't wan't him getting out the masking tape... Do you?
What tape are you talking about... we didn't even have a class today... RIGHT CLASS???
Nora, GREAT QUESTIONS, I thank you, the class thanks you, including Nick^2 and nit and wit.
As for your questions... 18 & 19 To help you with this, draw triangle ABC with vertex A lower left, vertex B lower right and vertex C up top somewhere. Angle A is OPPOSITE side (segment) BC, Angle B is OPPOSITE side AC and angle C is OPPOSITE side AB. It has NOTHING to do with exterior angles or supplementary angles, ca-peeesh?
For 26b, it is simply warning you that observing patterns isn't always going to work (you would THINK 6 points on a circle would create 32 regions based on the pattern, but the actual count was 31 - ask Nick, I'm sure he counted them TWICE). So, the book is simply warning you to use a deductive proof... that's like the ALL of the proofs we've been doing so far, using FACTS ... postulates, definitions and theorems... not just looking for patterns or reasonable answers. IT IS NOT EXPECTING YOU TO WRITE A PROOF FOR THIS PROBLEM!!
For #29, yup, I wouldn't describe it as "making triangles" but you are basically correct... diagonals are auxiliary lines that connect the vertices of a polygon.
pg 111 #4, you're over-thinking a bit, but you're CORRECT... line j can be skew to line r... but who cares about line s and line t? There is no need to make mention of them based on the question, ca-peeesh?
Nora... GREAT QUESTIONS... I can see that you took the assignment very seriously. Let me know which of my answers helped and which need more clarification... see you on Friday!
As for #30, you can find some triangles and quadrilaterals in that drawing, and you know something about the sum of their interior angles. It's a very interesting problem, I LOOK FORWARD TO NICK & KATE'S PRESENTATION!! DON'T YOU, TOO?? :)
I'm on page 110 number 7 and i got a negative number for one of my solutions. I plugged it back in and still got a negative number.
I also don't like number 13 on page 113. I think its something like line ED creates two congruent angles ABE and angle CDB. Then line DG bisects CDB and line FB bisects ABE. and since to lines bisect two congruent angles they create congruent corresponding angles. I don't know if that's right or not the answers aren't in the back of the book.
For pg 110 #7, you're in the endzone holding the ball... just spike it already!
Sounds like you gotsk two solutions, and one pair of sides didn't yield a solution. So, you found 2 values of 'x' that work... GOOD JOB!! Theoretically 'x' could be negative, but the resulting side length(s) cannot be negative.
Essentially, you wrote a paragraph proof... I would like to see if you could write it as a two-column proof, detailing ALL of the steps. That said, your interpretation of the problem clearly indicates understanding (I love that!).
WELL, I KNOW FOR SURE, IM NOT GOING TO BE PRESENTING!! anyway, for number 6 on page 110, i think we have to find factors..cause their like binomials? it brings back memories, but i can't seem to rememeber how to do it.PLEASE HELP!
You're overthinking it a bit... so even though FACTORING IS FUN & EASY, you don't need that for 110 #6, it's just some e-z alternating interior, supplementary and vertical angles that you need to see. Good luck!
i'm getting deductive and inductive reasoning mixed up. (classroom exercises page 107)
ReplyDeleteon number 18 page 108 when it says the angles opposite does it mean the supplementary angles?
same thing on number 19 what does the book mean by opposite?
on number 26b (page 108) it says write a deductive proof. What's a deductive proof?
on number 29 page 109 what's the number of diagonals (like what does it mean not what's the answer)? is that the number of auxiliary lines we can draw in a polygon to make triangles?
on page 109 number 30 i have no idea how to even get started with trying to figure out the measure of the angles.
and i just want to get one thing clear. okay so the sum of the exterior angles are always 360 no matter how many sides right?
i'm not sure about number 4 on the chapter review on page 111 i want to say no but i'm not entirely sure the r and s could be parallel and j could skew r and intersect with s and s and r would still be parallel
for 15 on page 111 i can say angle 2 is congruent to angle 8 but i dont know what the reason is
and that's all that i can find. i only read the problems i didnt do any yet so if i find any i'll blog it
Mr Chamberlain...could all the questions be like pg 110 #8?
ReplyDeleteMoy and Chisu
yeah i agree with moy and chisu those questions would make the test a fair challenge and most of us would get A's
ReplyDeleteYou mean you don't want to be miserable?
ReplyDeleteBut that would be horrible!
Have you not learned anything?
By inductive reasoning, whenever we aren't miserable, Mr.C gets mad. From here we would assume that if we do well on the test he will be mad. You don't wan't him getting out the masking tape... Do you?
What tape are you talking about... we didn't even have a class today... RIGHT CLASS???
ReplyDeleteNora, GREAT QUESTIONS, I thank you, the class thanks you, including Nick^2 and nit and wit.
As for your questions...
18 & 19 To help you with this, draw triangle ABC with vertex A lower left, vertex B lower right and vertex C up top somewhere. Angle A is OPPOSITE side (segment) BC, Angle B is OPPOSITE side AC and angle C is OPPOSITE side AB. It has NOTHING to do with exterior angles or supplementary angles, ca-peeesh?
For 26b, it is simply warning you that observing patterns isn't always going to work (you would THINK 6 points on a circle would create 32 regions based on the pattern, but the actual count was 31 - ask Nick, I'm sure he counted them TWICE). So, the book is simply warning you to use a deductive proof... that's like the ALL of the proofs we've been doing so far, using FACTS ... postulates, definitions and theorems... not just looking for patterns or reasonable answers. IT IS NOT EXPECTING YOU TO WRITE A PROOF FOR THIS PROBLEM!!
ReplyDeleteFor #29, yup, I wouldn't describe it as "making triangles" but you are basically correct... diagonals are auxiliary lines that connect the vertices of a polygon.
ReplyDeleteFor #29 & 30, I'm looking forward to Nick & Kate presenting the solutions in class!
ReplyDelete(Questions of that MAGNITUDE will not be on a test, but they are FUN to learn from)uhhh, don't count on pg 110 #8 being there either, btw
Re-read Thm 3-14 "... ANY CONVEX POLYGON..." remember when we did the proof today in class, the "n" from "n-sided" went hasta-la-bye-bye, yes?
ReplyDeletepg 111 #4, you're over-thinking a bit, but you're CORRECT... line j can be skew to line r... but who cares about line s and line t? There is no need to make mention of them based on the question, ca-peeesh?
ReplyDeletepg 111 #15... do a little digging in your G.B. and you should find the answers.
ReplyDeleteNora... GREAT QUESTIONS... I can see that you took the assignment very seriously. Let me know which of my answers helped and which need more clarification... see you on Friday!
ReplyDeleteI'm still getting deductive and inductive reasoning confused.
ReplyDeleteI still don't get #30 on page 109
I'm only on the self test 2 so more questions might come later :)
the comments were really helpful thanks!
I googled "DEDUCTIVE vs. INDUCTIVE REASONING EXAMPLES" and found this (among many others):
ReplyDeletehttp://www.sjsu.edu/depts/itl/graphics/induc/ind-ded.html
The Main Site looks interesting as well:
http://www.sjsu.edu/depts/itl/graphics
Some GREAT WEEKEND READING, eh?
As for #30, you can find some triangles and quadrilaterals in that drawing, and you know something about the sum of their interior angles. It's a very interesting problem, I LOOK FORWARD TO NICK & KATE'S PRESENTATION!! DON'T YOU, TOO?? :)
ReplyDeleteI'm on page 110 number 7 and i got a negative number for one of my solutions. I plugged it back in and still got a negative number.
ReplyDeleteI also don't like number 13 on page 113. I think its something like line ED creates two congruent angles ABE and angle CDB. Then line DG bisects CDB and line FB bisects ABE. and since to lines bisect two congruent angles they create congruent corresponding angles. I don't know if that's right or not the answers aren't in the back of the book.
For pg 110 #7, you're in the endzone holding the ball... just spike it already!
ReplyDeleteSounds like you gotsk two solutions, and one pair of sides didn't yield a solution. So, you found 2 values of 'x' that work... GOOD JOB!! Theoretically 'x' could be negative, but the resulting side length(s) cannot be negative.
For pg 113 #13, IT LIKES YOU!!
ReplyDeleteEssentially, you wrote a paragraph proof... I would like to see if you could write it as a two-column proof, detailing ALL of the steps. That said, your interpretation of the problem clearly indicates understanding (I love that!).
Who's presenting #30 tomorrow in class? Nick, Kate, Nora?? Anybody?
ReplyDeleteWELL, I KNOW FOR SURE, IM NOT GOING TO BE PRESENTING!! anyway, for number 6 on page 110, i think we have to find factors..cause their like binomials? it brings back memories, but i can't seem to rememeber how to do it.PLEASE HELP!
ReplyDeleteYou're overthinking it a bit... so even though FACTORING IS FUN & EASY, you don't need that for 110 #6, it's just some e-z alternating interior, supplementary and vertical angles that you need to see. Good luck!
ReplyDeleteIndeductive reasoning is easier than deductive reasoning!
ReplyDeleteIsn't that Postulate 1 of Viottoean Geometry?
ReplyDelete