Diane, thanks for the wrap up and reminding me why this discussion sounded familiar. Jonathan, there seems to be plenty of discussion and exploration of the inclusive vs. exclusive trapezoid. I remember the first discussion facilitated by Brian Cohen in Nov. 2012 AMTNY in Rye Brook (another good reason to meet your colleagues this Fall in Syracuse). Many of us requested a CCLS glossary or PARCC glossary or a NCTM CC glossary or a NYSED glossary (like 2005), I?m sure there will be a lot of volunteers for the ?T? section. Maybe we can all agree that a released, aligned glossary would be ideal.
From: firstname.lastname@example.org [mailto:email@example.com] On Behalf Of Jonathan Sent: Wednesday, May 28, 2014 1:31 PM To: firstname.lastname@example.org Subject: Re: trapezoid clarification
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. It has additional properties, but they flow from that definition.
How do we want to define an isosceles trapezoid? (I don't know, and it won't be our choice anyhow) If we say "a quadrilateral with exactly one pair of opposite sides parallel... we are doing something strange, given the inclusive definition of trapezoid that NYS is adopting without discussion. If we say "a quadrilateral with at least one pair of opposite sides parallel, and exactly one pair of opposite sides congruent" we are reintroducing an exclusive definition (but of something else) If we say "a trapezoid with one pair of opposite sides congruent" we are recognizing what "isosceles" means, but leaving the one pair/at least one pair question. This might be in the spirit of what NYS has just done, but it includes all parallelograms, and what we used to call isosceles trapezoids. This would dramatically change the list of properties. It is important to recognize that the properties will flow from the definition
Another option is to say "the word 'isosceles' does not apply cleanly to the trapezoid, as recently redefined. Let's stop talking about 'isosceles trapezoid'"
And then we could spend more time on kites, undisturbed by any arbitrary common core redefinition.
Jonathan Halabi the Bronx
On Wed, May 28, 2014 at 1:13 PM, Lisa Clark <email@example.com<mailto:firstname.lastname@example.org>> wrote: How is a rhombus an isosceles trapezoid? It doesn't have all the properties of an isosceles trap. Such as diagonals congruent, base angles congruent and Opposite angles supplementary.
A rhombus is a parallelogram because it has ALL the properties of a parallelogram and then has some of its own "special" properties. Somebody pease explain this.
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On May 28, 2014, at 5:52 AM, email@example.com<mailto:firstname.lastname@example.org> wrote: Grace Of course you are right and your summary of trapezoid clarifications are going to be helpful to anyone who was not sure about the implications of this revised definition. Good point of how it can be used in a proof. Bruce
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-----Original Message----- From: Grace Wilkie <email@example.com<mailto:firstname.lastname@example.org>> To: nyshsmath <email@example.com<mailto:firstname.lastname@example.org>> Sent: Tue, May 27, 2014 10:33 PM Subject: Re: trapezoid clarification
Inclusive, exclusive, reclusive ... hopefully there will be no questions either test ... you can't have one definition for the common core test and another definition for the regents test ... look at all the discussion we are having ... and there are plenty of teachers that don't even realize there is a different definition ... and we still have not fine tuned the isosceles trapezoid ... Here is what I get - but of course I could be wrong All parallelograms, rectangles, rhombuses and squares are trapezoids. Some trapezoids are parallelograms, rectangles, rhombuses and squares. All rectangles, rhombuses and squares are isosceles trapezoids. Some isosceles trapezoids are rectangles, rhombuses and squares. Proofs can now include the word 'trapezoid' ie. A rhombus is an isosceles trapezoid with the diagonals perpendicular to each other. I wish the state would come out with the conversion score key before the regents but I know that should happen but will not. I wish all parts of these tests were open to the public - we need to work on SED to make that happen ... if we expect to 1. help students then we need to know what they got wrong - not a topic but the question and the student response 2. help teachers improve instruction then we need to be informed what our students understood and did not understand 3. have faith that the tests are valid and reliable - we will never know if there are errors if we don't see them (there have been mistakes in the past).
I will have good thoughts for the students and teachers going through the common core test and possibly the regents. As always, Grace Wilkie
On Tue, May 27, 2014 at 10:36 AM, Elaine Zseller <EZseller@nasboces.org<mailto:EZseller@nasboces.org>> wrote: The inclusive definition of trapezoid would classify rectangles and squares as isosceles trapezoids. An Isosceles trapezoid has congruent base angles and at least one pair of parallel sides. Rectangles and squares fit these more restrictive criteria. All parallelograms are trapezoids but all parallelograms do not fit the more restrictive criteria of an isosceles trapezoid.
- -----Original Message----- From: email@example.com<mailto:firstname.lastname@example.org> [mailto: email@example.com<mailto:firstname.lastname@example.org>] On Behalf Of Jennifer Sauer Sent: Sunday, May 25, 2014 9:38 PM To: email@example.com<mailto:firstname.lastname@example.org> Subject: Re: trapezoid clarification According to the website below, when using the inclusive definition of a trapezoid, an isosceles trapeziod is still defined as a "strict" trapezoid (exclusive definition) with congruent legs. Therefore squares and rectangles would not be included. Does that agree with the CCSS definition?