HSDCY Posted November 17, 2008 Share Posted November 17, 2008 I found two different definitoins. In some math websites, they define it as "a quadrilateral that has at least one pair of parallel lines". But in Singapore math 5B HIG, it is difined as "a quadrilateral with a pair of unequal parallel sides". Which one is right? Ds's EPGY program asks: Is every parallelogram a trapezoid? If you use the first definition, the answer is yes. But if you use the second definition then the answer is no. What do you think? Quote Link to comment Share on other sites More sharing options...
AnnetteB Posted November 17, 2008 Share Posted November 17, 2008 (edited) Saxon Advanced Mathematics says, "a parallelogram is a 4-sided polygon in which both pairs of opposite sides are parallel. A trapezoid is a four-sided polygon which has exactly one pair of parallel sides." So, both of them are quadrilaterals, but they are not subsets of each other. Edited November 17, 2008 by AnnetteB I got distracted before I completed my thought...it happens Quote Link to comment Share on other sites More sharing options...
kiana Posted November 18, 2008 Share Posted November 18, 2008 Can you figure out what definition EPGY is using? That is what will give you the "right" answer. Different programs define it in different ways, but I have always heard it defined as a quadrilateral with at least two parallel sides. Quote Link to comment Share on other sites More sharing options...
kokotg Posted November 18, 2008 Share Posted November 18, 2008 DH, the math teacher, says that there is not so much a standard definition with such things. "It depends," he says, "on whether you consider trapezoids to be a subset of parallelograms." It turns out he has actually had this conversation with his mathematician father before. DH prefers the second definition; his father made an argument for the first one. So, in short, you have to agree on a definition before you can answer the question. I'm kind of sorry I asked now. DH got really excited and talked about it for a long time. Quote Link to comment Share on other sites More sharing options...
HSDCY Posted November 18, 2008 Author Share Posted November 18, 2008 According to EPGY, every parallelogram is a trapezoid. The program did not give us their definition for a trapezoid, but apparently they are using the first definition. From your posts I see that there is no "right" definition for trapezoids. I was under the impression that math did not have these gray areas but I guess I was wrong. Now I wonder why mathematicians can't agree on what a trapezoid is..... Quote Link to comment Share on other sites More sharing options...
riutwpoj Posted November 18, 2008 Share Posted November 18, 2008 A trapezoid is a four-sided polygon which has exactly one pair of parallel sides. BY the way, the lengths of the two parallel side are always not same. Quote Link to comment Share on other sites More sharing options...
MyThreeSons Posted November 18, 2008 Share Posted November 18, 2008 A trapezoid is a four-sided polygon which has exactly one pair of parallel sides. and I've always used the above definition. If the parallel sides are congruent, it automatically becomes a parallelogram and is not a trapezoid. Quote Link to comment Share on other sites More sharing options...
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