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Q&A #838


Definition of a kite

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 24, 1998 at 21:29:05
Subject: Re: Definition of a kite

Hi, Cindy,

If your text defines a kite in this manner then all of the answers in the 
book will be keyed to this definition. If you wish for a rhombus to be a kite
then you would be giving a different definition to kite.

The purpose of definitions is so that individuals will be able to apply them 
and communicate with each other. I suggest that if you allow the omission of 
"disjoint" from your definition, determine if all of the properties of a kite 
that you have derived also are applicable to a rhombus. If they are, then a 
rhombus is a special kite with two pairs of equal sides that are not
disjoint. In rhombus ABCD: AB = BC and BC = CD  where BC occurs in both pairs.

What I find very interesting is to allow a class to determine their own 
definitions and build the system of quadrilaterals using their definitions.  
One of the categories to define is trapezoid.

"A quadrilateral with exactly one pair of sides parallel is a trapezoid."

If you leave out "exactly" then a parallelogram is also a special case of a 
trapezoid. My only advice to you is: once you agree upon a definition do 
not change it!

 -Marielouise, for the Teacher2Teacher service

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