mathmath333
  • mathmath333
Question maths/reasoning
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathmath333
  • mathmath333
|dw:1439124280221:dw|
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{In the figure: }\hspace{.33em}\\~\\ & \normalsize \text{K represents all Kites}\hspace{.33em}\\~\\ & \normalsize \text{Q represents all Quadrilaterals}\hspace{.33em}\\~\\ & \normalsize \text{R represents all Rhombus}\hspace{.33em}\\~\\ & \normalsize \text{P represents all Parallelogram}\hspace{.33em}\\~\\ & \normalsize \text{The statement "Rhombus is also a Kite"}\hspace{.33em}\\~\\ & \normalsize \text{can be described as}\hspace{.33em}\\~\\ & 1.) \normalsize \text{P and K is nothing but R}\hspace{.33em}\\~\\ & 2.) \normalsize \text{P or K is nothing but R}\hspace{.33em}\\~\\ & 3.) \normalsize \text{P and R is nothing but K}\hspace{.33em}\\~\\ & 4.) \normalsize \text{P or R is nothing but K}\hspace{.33em}\\~\\ \end{align}}\)
ganeshie8
  • ganeshie8
|dw:1439124864364:dw|

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ganeshie8
  • ganeshie8
we represent common region using "\(\cap\)" and read it out as "\(\text{and}\)"
mathmath333
  • mathmath333
ok
ganeshie8
  • ganeshie8
In above venn diagram, we have \[P \text{ and } K = R\]
ganeshie8
  • ganeshie8
therefore a \(R\)hombus is both a \(P\)arallelogram and a \(K\)ite
ganeshie8
  • ganeshie8
Rhombus belongs to both the families of Parallelogram and Kite
mathmath333
  • mathmath333
1st option is correct ?
mathmath333
  • mathmath333
???
ganeshie8
  • ganeshie8
Yep!
mathmath333
  • mathmath333
great!
mathstudent55
  • mathstudent55
Given the Venn diagram in the question, I agree with @ganeshie8, but are we allowed to suspend the correct definitions of the terms used, so the problem works? A kite can never be a rhombus or a parallelogram, and a rhombus can never be a kite using the normal definitions of those quadrilaterals.
ganeshie8
  • ganeshie8
A square is also a rhombus/rectangle/parallelogram/trapezoid/kite A rhombus is also a parallelogram/trapezoid/kite so, some kites are also squares/rhombii/parallelograms I don't see any conflict here, @mathstudent55
mathmath333
  • mathmath333
this is purely reasoning type question
ganeshie8
  • ganeshie8
|dw:1439128107280:dw|
mathmath333
  • mathmath333
didnt memtion kites
ganeshie8
  • ganeshie8
you can fill it up
ganeshie8
  • ganeshie8
does a square satisfy the properties of a kite ?
mathmath333
  • mathmath333
yes
ganeshie8
  • ganeshie8
so, some kites are squares. does a rhombus satisfy the properties of a kite ?
mathmath333
  • mathmath333
yes
ganeshie8
  • ganeshie8
since a square is also a rhombus, parallelogram and trapezoid, it follows that some kites are rhombii/parallelograms/trapezoids
mathstudent55
  • mathstudent55
Then perhaps I never learned the definition of kite correctly. I thought a kite is a quadrilateral with a pair of two pairs of congruent adjacent sides, both pairs not being congruent to each other. If the definition of kite allows for the two pairs of adjacent sides to be congruent, making all sides congruent, then a rhombus is indeed a special case of a kite, and certainly a kite can be a square.
mathstudent55
  • mathstudent55
Now since you mention a trapezoid, there is another problem. My understanding of a trapezoid is that it's a quadrilateral with exactly one pair of parallel opposite sides. This means the second pair of opposite sides cannot be parallel, and therefore a trapezoid and a parallelogram are mutually exclusive quadrilaterals.
ganeshie8
  • ganeshie8
i remember them as : A kite is just a quadrilateral with two pairs of congruent adjacent sides. A trapezoid is a quadrilateral with at least one pair of parallel sides I am also googling for correct definitions as we speak...
ganeshie8
  • ganeshie8
|dw:1439129024111:dw|
ganeshie8
  • ganeshie8
some online materials do say that a trapezoid must have "exactly" one pair of parallel sides |dw:1439129281970:dw|
mathstudent55
  • mathstudent55
Allowing a kite to have all 4 sides congruent makes the original Venn diagram of the problem completely acceptable. I just have to get used to the correct definition of a kite.
mathstudent55
  • mathstudent55
Yes, and some websites state that a trapezoid has at least one pair of sides parallel. In addition, there seems to be different usage for trapezoid and trapezium in the U.S. and the UK.
ganeshie8
  • ganeshie8
I remember facing issues with trapezoid and trapezium before haha
mathstudent55
  • mathstudent55
U.S. trapezoid = UK trapezium (quadrilateral with either exactly or at least 1 pair of sides parallel) U.S. trapezium = UK trapezoid (quadrilateral with no sides parallel)
mathstudent55
  • mathstudent55
@ganeshie8 As always, thanks for your insight.

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