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Topic: trapezoid clarification
Replies: 55   Last Post: Apr 24, 2017 2:30 PM

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 Virginia Kuryla Posts: 61 Registered: 1/26/06
Re: trapezoid clarification
Posted: Jun 16, 2014 6:39 PM
 att1.html (13.7 K)

Found some interesting reading on the subject mathematical definitions that
includes discussion about trapezoids. I stumbled on them by checking the
references on wikipedia. I am always suspicious of things on wikipedia and
always like to check the sources for myself. I'll let you make your own
decisions. :)

http://en.wikipedia.org/wiki/Isosceles_trapezoid

The Role and Function of Hierarchical Classification by Michael deVilliers
Published in *For the Learning of Mathematics* 14,1 (February 1994)
Vancouver, British Columbia
http://mzone.mweb.co.za/residents/profmd/classify.pdf

I think I'll have to read them more thoroughly this summer, but I find the
ideas presented intriguing.

Ginny Kuryla

On Thu, Jun 5, 2014 at 12:25 PM, Grace Wilkie <gwilkie@highlands.com> wrote:

> I agree with Roberta ... we need clarifications ... SED has now defined
> trapezoid but they have not defined isosceles trapezoid or what theorems
> will be associated with it ... I would also appreciate a diagram with the
> isosceles trapezoid included.
>
> I respectfully disagree with CCSIMath ... a mathematical definition is not
> picayune - it is this foundation on which theorems are based. NYSED is not
> stirring the cauldron - it is the everyday mathematics teacher who is ...
> they are being responsible and due diligent for their students ... I hope
> other states benefit from our discussions and outcomes.
>
> As always,
> Grace Wilkie
>
>
>
>
>
>
> On Tue, Jun 3, 2014 at 10:47 PM, Roberta Eisenberg <bobbi@alumni.nd.edu>
> wrote:
>

>> The property that you mention is a thm that follows from the def of isos
>> trap using the exclusive defn. (An isos trap is a trap whose non-// sides
>> are congruent.)
>>
>> NYS must supply teachers and students with a complete list of definitions
>> and not only the one inclusive def. of trap. How do they define isos trap
>> with the inclusive def of trap? And what thms about isos traps follow from
>> whatever def is supplied to us?
>>
>> Someone supplied a def of isos trap about a week ago, but does NYS accept
>> that?
>>
>> Bobbi
>>
>> On Jun 3, 2014, at 9:31 PM, Elaine Zseller <EZseller@nasboces.org> wrote:
>>
>> All rhombuses are not isosceles trapezoids. Isosceles trapezoids have
>> their base angles congruent. Only the rhombus known as a square fits that
>> definition.
>>
>> *From:* owner-nyshsmath@mathforum.org [
>> mailto:owner-nyshsmath@mathforum.org <owner-nyshsmath@mathforum.org>] *On
>> Behalf Of*bcwaldner@aol.com
>> *Sent:* Wednesday, May 28, 2014 5:52 AM
>> *To:* nyshsmath@mathforum.org
>> *Subject:* Re: trapezoid clarification
>>
>> 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
>>
>> Sent from AOL Mobile Mail
>>
>>
>> -----Original Message-----
>> From: Grace Wilkie <gwilkie@highlands.com>
>> To: nyshsmath <nyshsmath@mathforum.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>
>> 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: owner-nyshsmath@mathforum.org [mailto:owner-nyshsmath@mathforum.org]
>> On Behalf Of Jennifer Sauer
>> Sent: Sunday, May 25, 2014 9:38 PM
>>
>> To: nyshsmath@mathforum.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?
>>
>>
>>
>> http://www.math.washington.edu/~king/coursedir/m444a00/syl/class/trapezoids/Trapezoids.html
>>
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>>
>>

>

--
*Virginia Kuryla*