I was watching some of the video tutors from #4-1, and why would you need to prove all parts of a triangle congruent (sides & angles) if there are postulates and theorems you can use to skip all of that?
I'm not sure how to do #17 on the quiz.. How am I sure to put the right sides in the right spaces using the correct angle measures with just a protractor and straightedge? I'm confused!
While doing #6-#11, I couldn't find ONE that had "not enough info", they are seemed to have enough to use a postulate or theorem.. That makes me suspicious; is there one without enough information?
One of the challenges in Geometry is that it is taught in a logical and linear fashion. One learning builds to the next. We can't start talking about SAS and ASA before we define the very meaning of congruent figures. So section 4-1 is a building block that does just that (see the defn of congruent polygons)... it let's us know that CPCPC... Corresponding Parts of Congruent Polygons are Congruent. One natural subset of this statement is CPCTC (Corr Parts of Cong Triangles are Cong.).
Once we accept this definition, THEN we can move forward to see that, oh my gosh by golly, we don't really need to know that all six corresponding parts of two triangles need to match up in order to state congruence, we can see INDUCTIVELY (by observation of many different attempts - remember our "flexi-straws" day) that if certain key parts are congruent, i.e. SSS, SAS, and ASA, then, AND ONLY THEN, the triangles can also be designated as congruent.
It's a building process... the Greeks didn't have flexi-straws, but they used their rope-stretchers (and ultimately compasses and straight-edges) to state their postulates and prove their theorems.
I'm not sure how to do #17 on the quiz.. How am I sure to put the right sides in the right spaces using the correct angle measures with just a protractor and straightedge? I'm confused!
While doing #6-#11, I couldn't find ONE that had "not enough info", they are seemed to have enough to use a postulate or theorem.. That makes me suspicious; is there one without enough information?
Did you use the word "protractor" for the construction problem??!! The poor rope-strethers are turning in their tombs!! Compass and straight-edge only... measuring angles with a protractor is for the Macedonians!!
I was watching some of the video tutors from #4-1, and why would you need to prove all parts of a triangle congruent (sides & angles) if there are postulates and theorems you can use to skip all of that?
ReplyDelete^ (To prove the triangles' congruence, I forgot to say)
ReplyDeleteWill there be a question like #21 on the quiz? Because I don't really understand it..
ReplyDeleteI'm not sure how to do #17 on the quiz.. How am I sure to put the right sides in the right spaces using the correct angle measures with just a protractor and straightedge? I'm confused!
ReplyDeleteWhile doing #6-#11, I couldn't find ONE that had "not enough info", they are seemed to have enough to use a postulate or theorem.. That makes me suspicious; is there one without enough information?
ReplyDeleteDear 4-1,
ReplyDeleteOne of the challenges in Geometry is that it is taught in a logical and linear fashion. One learning builds to the next. We can't start talking about SAS and ASA before we define the very meaning of congruent figures. So section 4-1 is a building block that does just that (see the defn of congruent polygons)... it let's us know that CPCPC... Corresponding Parts of Congruent Polygons are Congruent. One natural subset of this statement is CPCTC (Corr Parts of Cong Triangles are Cong.).
Once we accept this definition, THEN we can move forward to see that, oh my gosh by golly, we don't really need to know that all six corresponding parts of two triangles need to match up in order to state congruence, we can see INDUCTIVELY (by observation of many different attempts - remember our "flexi-straws" day) that if certain key parts are congruent, i.e. SSS, SAS, and ASA, then, AND ONLY THEN, the triangles can also be designated as congruent.
It's a building process... the Greeks didn't have flexi-straws, but they used their rope-stretchers (and ultimately compasses and straight-edges) to state their postulates and prove their theorems.
Good question.
Mr. C.
Well, pg 243 #21 is a good discussion question... not likely to be found on a test... if that's your only issue you're in GREAT SHAPE!!
ReplyDeleteLet's remember to discuss it in class.
Okay, thanks!
ReplyDeleteAnd what about #17??
And #6-#11?
ReplyDeleteSorry, I need more specific questions... I refuse to believe that you have NO CLUE.
ReplyDeleteI said these above, I guess they don't show up??
ReplyDeleteI'm not sure how to do #17 on the quiz.. How am I sure to put the right sides in the right spaces using the correct angle measures with just a protractor and straightedge? I'm confused!
While doing #6-#11, I couldn't find ONE that had "not enough info", they are seemed to have enough to use a postulate or theorem.. That makes me suspicious; is there one without enough information?
For #6-11, I would have had the same suspicion... however you are wrong... you are right!
ReplyDelete6) ASA
7) SSS
8) SAS
9) AAS
10) SAS
11) AAS
For #6-#11.. Yay!
ReplyDeleteI have a new toy!!! Whaddya think?!
ReplyDeleteclick here-> Construction Using SSS
Did you use the word "protractor" for the construction problem??!! The poor rope-strethers are turning in their tombs!! Compass and straight-edge only... measuring angles with a protractor is for the Macedonians!!
ReplyDelete