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.
Sorry, my last comment just had half the text cut out of it, so here we go again. On #9 on pg 207, I got to M<ROT=m<ROS+M<SOT, and the same relative stuff for <SOV. Now I see whats going on here, but I don't know what property of inequality should be used or if more steps are needed.
The properties of inequality are as fickle as Simon the Cat. Please REREAD the bottom of page 203 and I quote (with CAPS for EM-PHAH-SIS)
The properties of inequality you will use MOST OFTEN in geometry are stated on the following page... blah blah blah...
Nick's comment above, and I quote:
"If only there was a property (of inequality) like: If a>b and c is a real number, a+c>b+c
(btw, Charmi, notice Nick's misuse of the colon (:); it should follow the word "like" immediately, without a space)
Nick, your wish is the math god's command. Any property of equality (POE) can be turned into a property of inequality (POI), as long as we can deem it to be true in all cases.
You just need to make one small change to your POI:
If a>b and c is a POSITIVE real number, a+c>b+c
This new POI fills the bill perfectly for #9, since we're talking about angle measures, which are always POSITIVE.
Moral of the story: A POI in time, saves nine!
Ciao for now, Mr. C.
P.S. For those that need them, I will sell POI's for $10 (quiz price), $20 (unit test price) and $50 (mid-term special).
Sorry, my last comment just had half the text cut out of it, so here we go again. On #9 on pg 207, I got to M<ROT=m<ROS+M<SOT, and the same relative stuff for <SOV. Now I see whats going on here, but I don't know what property of inequality should be used or if more steps are needed.
ReplyDeleteIf only there was a property like :If a>b and c is a real number, a+c>b+c
ReplyDeleteThat, for some reason wouldn't fit in the last entry.
The properties of inequality are as fickle as Simon the Cat. Please REREAD the bottom of page 203 and I quote (with CAPS for EM-PHAH-SIS)
ReplyDeleteThe properties of inequality you will use MOST OFTEN in geometry are stated on the following page... blah blah blah...
Nick's comment above, and I quote:
"If only there was a property (of inequality) like: If a>b and c is a real number, a+c>b+c
(btw, Charmi, notice Nick's misuse of the colon (:); it should follow the word "like" immediately, without a space)
Nick, your wish is the math god's command. Any property of equality (POE) can be turned into a property of inequality (POI), as long as we can deem it to be true in all cases.
You just need to make one small change to your POI:
If a>b and c is a POSITIVE real number, a+c>b+c
This new POI fills the bill perfectly for #9, since we're talking about angle measures, which are always POSITIVE.
Moral of the story: A POI in time, saves nine!
Ciao for now,
Mr. C.
P.S. For those that need them, I will sell POI's for $10 (quiz price), $20 (unit test price) and $50 (mid-term special).