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mathmath333

  • one year ago

Question maths/reasoning

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  1. mathmath333
    • one year ago
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    |dw:1439124280221:dw|

  2. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{In the figure: }\hspace{.33em}\\~\\ & \normalsize \text{K represents all Kites}\hspace{.33em}\\~\\ & \normalsize \text{Q represents all Quadrilaterals}\hspace{.33em}\\~\\ & \normalsize \text{R represents all Rhombus}\hspace{.33em}\\~\\ & \normalsize \text{P represents all Parallelogram}\hspace{.33em}\\~\\ & \normalsize \text{The statement "Rhombus is also a Kite"}\hspace{.33em}\\~\\ & \normalsize \text{can be described as}\hspace{.33em}\\~\\ & 1.) \normalsize \text{P and K is nothing but R}\hspace{.33em}\\~\\ & 2.) \normalsize \text{P or K is nothing but R}\hspace{.33em}\\~\\ & 3.) \normalsize \text{P and R is nothing but K}\hspace{.33em}\\~\\ & 4.) \normalsize \text{P or R is nothing but K}\hspace{.33em}\\~\\ \end{align}}\)

  3. ganeshie8
    • one year ago
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    |dw:1439124864364:dw|

  4. ganeshie8
    • one year ago
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    we represent common region using "\(\cap\)" and read it out as "\(\text{and}\)"

  5. mathmath333
    • one year ago
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    ok

  6. ganeshie8
    • one year ago
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    In above venn diagram, we have \[P \text{ and } K = R\]

  7. ganeshie8
    • one year ago
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    therefore a \(R\)hombus is both a \(P\)arallelogram and a \(K\)ite

  8. ganeshie8
    • one year ago
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    Rhombus belongs to both the families of Parallelogram and Kite

  9. mathmath333
    • one year ago
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    1st option is correct ?

  10. mathmath333
    • one year ago
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    ???

  11. ganeshie8
    • one year ago
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    Yep!

  12. mathmath333
    • one year ago
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    great!

  13. mathstudent55
    • one year ago
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    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.

  14. ganeshie8
    • one year ago
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    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

  15. mathmath333
    • one year ago
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    this is purely reasoning type question

  16. ganeshie8
    • one year ago
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    |dw:1439128107280:dw|

  17. mathmath333
    • one year ago
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    didnt memtion kites

  18. ganeshie8
    • one year ago
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    you can fill it up

  19. ganeshie8
    • one year ago
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    does a square satisfy the properties of a kite ?

  20. mathmath333
    • one year ago
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    yes

  21. ganeshie8
    • one year ago
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    so, some kites are squares. does a rhombus satisfy the properties of a kite ?

  22. mathmath333
    • one year ago
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    yes

  23. ganeshie8
    • one year ago
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    since a square is also a rhombus, parallelogram and trapezoid, it follows that some kites are rhombii/parallelograms/trapezoids

  24. mathstudent55
    • one year ago
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    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.

  25. mathstudent55
    • one year ago
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    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.

  26. ganeshie8
    • one year ago
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    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...

  27. ganeshie8
    • one year ago
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    |dw:1439129024111:dw|

  28. ganeshie8
    • one year ago
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    some online materials do say that a trapezoid must have "exactly" one pair of parallel sides |dw:1439129281970:dw|

  29. mathstudent55
    • one year ago
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    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.

  30. mathstudent55
    • one year ago
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    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.

  31. ganeshie8
    • one year ago
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    I remember facing issues with trapezoid and trapezium before haha

  32. mathstudent55
    • one year ago
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    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)

  33. mathstudent55
    • one year ago
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    @ganeshie8 As always, thanks for your insight.

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