# Thread: Quadrilateral Family: In nice and green valley there is a building with 4 floors...

1. ## Quadrilateral Family: In nice and green valley there is a building with 4 floors...

In nice and green valley there is a building with 4 floors.
In every floor there is a quadrilateral polygons, that is have a unique property.
Which quadrilateral polygons are in the building?

The answer is: Square, Rhombus, Trapezoid and Kite.

the answer of square I understood because a unique rectangle that has sizes that are equal.

Why the rest are living the building?

2. Originally Posted by shahar
In nice and green valley there is a building with 4 floors.
In every floor there is a quadrilateral polygons, that is have a unique property.
Which quadrilateral polygons are in the building?

The answer is: Square, Rhombus, Trapezoid and Kite.

the answer of square I understood because a unique rectangle that has sizes that are equal.

Why the rest are living the building?
Are you serious?

A rhombus is defined in geometery as a quadrilateral, all the sides of which are equal. A square is a rhombus that is also a rectangle.

A trapezoid is defined in geometry as a quadrilateral, with one pair of parallel sides.

I am not aware that "kite" has a technical definition in mathematics. The wing of a common kind of kite in the U.S. is a quadrilateral with one pair of touching sides of length x and another pair of touching sides of length y, where x > y. Thus, it is not a rhombus (all sides are not equal), nor is it a trapezoid (it has no parallel sides).

3. ## What is kite

By Kite word, I meant to quadrilateral polygon that in Hebrew is called Dalton = two equal-sizes triangles (isosceles triangle) that have a shared side like the kite game.

What is the word of isosceles triangles that have a common side and create a quadrilateral?

4. Originally Posted by shahar
By Kite word, I meant to quadrilateral polygon that in Hebrew is called Dalton = two equal-sizes triangles (isosceles triangle) that have a shared side like the kite game.

What is the word of isosceles triangles that have a common side and create a quadrilateral?
There may be a word that means a quadrilateral formed by two non-congruent isosceles triangles with a common base, but I do not know it. I also tutor at English Learners Stack Exchange so if such a word exists in English, it is not common. Probably, I would say "kite-shaped quadrilateral," which would get across the idea of "dalton" to a mathematician who is a native English speaker.

I have edited my first post.

5. Originally Posted by shahar
In nice and green valley there is a building with 4 floors.
In every floor there is a quadrilateral polygons, that is have a unique property.
Which quadrilateral polygons are in the building?

The answer is: Square, Rhombus, Trapezoid and Kite.

the answer of square I understood because a unique rectangle that has sizes that are equal.

Why the rest are living the building?
The word "kite", though non-technical, is easy enough to understand.

What I am unsure of is the meaning of "unique property". Can you explain what you think that means?

The whole question, of course, sounds silly; is it intended for children, perhaps? What is its context and source? Is there anything to suggest why they would give the answer they do?

The fact is that all the various kinds of quadrilateral are related, one being a special case of another. None are "unique" in an absolute sense, as I see it.

Your English grammar is often imperfect, as I'm sure you know; you mix up singular and plural, for example, which can make it hard to be sure what you mean, and here you have used the word "size" where I think you meant "side". I am wondering if that is happening here. Can you quote the problem word for word as given to you, in the original language, so we can judge its meaning better?

6. ## Here it is

השאלה היא:
בעמק יפה בין כרמים ושדות עומד בניין בן 4 קומות. חברו להם 4 מרובעים וביקשו להיות בו דיירים. התכנסו והעלו מחשבות כיצד יתפזרו בין הקומות. ואז עלה רעיון: זה שיהיה הראשון שיכריז על תכונה ייחודית - כל הקומה תהיה שלו.

התשובה היא: דלתון, טרפז, מעוין וריבוע .

7. ## I don't know if the lanauge is O.K. so I use google translate

the question is:
In a beautiful valley between vineyards and fields stands a four-story building. They were joined by four quarters and asked to be tenants. They gathered and thought about how they would spread between the floors. And then an idea came up: it would be the first to declare a unique feature-the whole floor would be his.

The answer is: Dalton, trapeze, rhombus and square.

8. Originally Posted by shahar
In nice and green valley there is a building with 4 floors.
In every floor there is a quadrilateral polygons, that is have a unique property.
Which quadrilateral polygons are in the building?

The answer is: Square, Rhombus, Trapezoid and Kite.

the answer of square I understood because a unique rectangle that has sizes that are equal.

Why the rest are living the building?
Originally Posted by shahar
the question is:
In a beautiful valley between vineyards and fields stands a four-story building. They were joined by four quarters and asked to be tenants. They gathered and thought about how they would spread between the floors. And then an idea came up: it would be the first to declare a unique feature-the whole floor would be his.

The answer is: Dalton, trapeze, rhombus and square.
Thanks. I, too, tried Google translate, and another site or two. Here is my attempt to put everything together to make a more meaningful version:

In a beautiful valley between vineyards and fields stands a four-story building. Four quadrilaterals came and asked to be tenants. They gathered and thought about how they would divide themselves between the floors. And then an idea came up: the first to declare a unique property, would get the whole floor.
The answer is: kite, trapezoid, rhombus and square.

Does that sound like a reasonable representation of the Hebrew?

I am thinking that perhaps it is the order of the four that is important, since as I interpret it, just the four came, and they needed to assign floors (rather than that four of all possible quadrilaterals are allowed in). So perhaps they are ordered by the number of properties they have. Another possibility, though, is that the answer is meant to be a list of categories into which everything would fit. (Neither of these ideas makes perfect sense to me.)

Clearly, though, the problem is still unclear, and is perhaps meant to be a riddle. But, also, a proper answer ought to include the reasons.

You haven't yet told us the context of the question. What type of source does it come from (e.g. children's book, contest problem, geometry textbook, ...)? Is there a picture with it? That may also help in interpreting it.

9. ## Here is the source

The flour need to accommodate by each 4-gon that have the unique properties that no others figure have.

In the article(now when I read it again), the 4-gons that I mentioned are the extreme figure in the hierarchy in the 4-gons family.
I repeat by the figures that in last in hierarchy.

(the hierarchy tree)
But why it so?!.... ?!

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