But now that I think about it, I should have said that a parallelogram is a special type of trap ? the kind with two pairs of // sides.
The question about isosceles trapezoids that someone raised in this thread, particularly about the base angles, has been on my mind. I can?t remember how that was dealt with back in the early 60s when I taught that honors geom class I mentioned the other day. In order to keep the thm. about the base angles, the def of isos. trap would have to say that it is a trap with only one pair of // sds.
What a can of worms this def. is!
Bobbi On May 18, 2014, at 8:36 PM, Kathy Noftsier <firstname.lastname@example.org> wrote:
> Wouldn't that be a parallelogram is a special type of trapezoid. Under this definition all parallelograms would be trapezoids but not all trapezoids would be parallelograms? > > Kathy Noftsier > ----- Original Message ----- > From: Roberta Eisenberg > To: AMTNYS HS listserv > Sent: Sunday, May 18, 2014 11:43 AM > Subject: Re: trapezoid clarification > > Yes, that is one of the theorems that follow from the definition. > > Under the inclusive def., just as a sq. is a special type of rhombus or rectangle, a trap. is a special type of parallelogram. > > I am not in favor, one way or the other, of either def. Mathematics is all about making defs. and then living with them. What I am definitely NOT in favor of is confusing students who have learned one def. (how long ago depends on what grade they are in now). > > Our job is to clarify the structure of this game we play, called mathematics, which starts with undefined terms, proceeds to definitions, and then proves theorems. > > All games have rules. Change the rules and you change the game. For example, in baseball, three strikes are out. But in my family, when we played wiffle ball games with adults and children, we let children have as many swings as they needed while the adults were limited to two. Tinker with Euclid?s 5th postulate and you get non-Euclidean geometries. > > Bobbi > > On May 18, 2014, at 10:33 AM, Wayne Barr <email@example.com> wrote: > >> >> Doesn't a parallelogram have opposite parallel sides with the parallel sides the same length? >> From: firstname.lastname@example.org <email@example.com> on behalf firstname.lastname@example.org <email@example.com> >> Sent: Sunday, May 18, 2014 8:12 AM >> To: firstname.lastname@example.org >> Subject: Re: trapezoid clarification >> >> Yes. A parallelogram is a trapezoid. I would like to see the clarifications but until they come we might want to look to earlier grades where they are defining these shapes. They have a venom diagram in the 5 th grade modules that show parallelograms are trapezoids. >> Michelle >> >> Sent from my iPhone >> >> On May 17, 2014, at 4:25 PM, JFish@csufsd.org wrote: >> >>> >>> So are you claiming that a parallelogram IS a trapezoid?????????? >>> >>> Jim >>> >>> -----email@example.com wrote: ----- >>> To: "<firstname.lastname@example.org>" <email@example.com> >>> From: Gene Jordan >>> Sent by: firstname.lastname@example.org >>> Date: 05/17/2014 04:11PM >>> Subject: Re: trapezoid clarification >>> >>> Here's the chart. >>> >>> I thought there was a trapezoid thread earlier, the geometry standards clarification document has it there. It should be released soon. >>> >>> I think Euclid defined Trapezoia as "all other quads". I tweeted the above image with the hope the end of the trapezoid wars was near. I remain neutral on inclusive or exclusive superiority, but would always appreciate our continued request for releasing a CCLS glossary to help us with precise language. >>> Sorry for my brevity ( and imprecision) it's a cool yet beautiful day to be outside. >>> >>> >>> ~Gene Jordan >>> >>> Broome County AMTNYS chair (Southern Tier) >>> >>> >>> On May 17, 2014, at 8:35 AM, "Meg Clemens" <email@example.com> wrote: >>> >>>> At training in Albany this past week, NYSED released a standards clarification document for Geometry that states (among other items) that a trapezoid is now defined with the ?inclusion? definition: a trapezoid has at least one pair of parallel sides. Although this might be a surprise to NYS teachers who have used the exclusive definition, this is a common definition for trapezoid. >>>> >>>> Three questions: >>>> >>>> 1. Is this standards clarification memo posted on engageny anywhere yet? I couldn?t find it. >>>> >>>> 2. How do we treat conflicting definitions next year when we are preparing students for both regents? >>>> >>>> 3. With the new definition, what is an isosceles trapezoid? I think we need clarification on this. >>>> >>>> a. If I use trapezoid w/ one pair of opposite sides congruent, then a parallelogram is an isosceles trapezoid but its base angles are not congruent. >>>> b. If I use trapezoid w/ one pair of opposite sides congruent and base angles are congruent, then rectangles and squares are isosceles trapezoids, which might be OK. >>>> c. There is an alternative definition that uses one axis of symmetry and one w/ no symmetry to yield the usual depiction of an isosceles trapezoid. >>>> >>>> >>>> Meg Clemens >>>> Canton Central School >>> >>> Spam >>> Not spam >>> Forget previous vote >>> >>> >>> [attachment "image.png" removed by James Fish/Teachers/CheektowagaSloan/Erie1] >>> [attachment "image.jpeg" removed by James Fish/Teachers/CheektowagaSloan/Erie1] >>> ******************************************************************* * To unsubscribe from this mailing list, email the message * "unsubscribe nyshsmath" to firstname.lastname@example.org * * Read prior posts and download attachments from the web archives at * http://mathforum.org/kb/forum.jspa?forumIDg1******************************************************************* > >