## mathmath333 one year ago Question maths/reasoning

1. mathmath333

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2. 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}}

3. ganeshie8

|dw:1439124864364:dw|

4. ganeshie8

we represent common region using "$$\cap$$" and read it out as "$$\text{and}$$"

5. mathmath333

ok

6. ganeshie8

In above venn diagram, we have $P \text{ and } K = R$

7. ganeshie8

therefore a $$R$$hombus is both a $$P$$arallelogram and a $$K$$ite

8. ganeshie8

Rhombus belongs to both the families of Parallelogram and Kite

9. mathmath333

1st option is correct ?

10. mathmath333

???

11. ganeshie8

Yep!

12. mathmath333

great!

13. 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.

14. 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

15. mathmath333

this is purely reasoning type question

16. ganeshie8

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17. mathmath333

didnt memtion kites

18. ganeshie8

you can fill it up

19. ganeshie8

does a square satisfy the properties of a kite ?

20. mathmath333

yes

21. ganeshie8

so, some kites are squares. does a rhombus satisfy the properties of a kite ?

22. mathmath333

yes

23. ganeshie8

since a square is also a rhombus, parallelogram and trapezoid, it follows that some kites are rhombii/parallelograms/trapezoids

24. 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.

25. 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.

26. 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...

27. ganeshie8

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28. ganeshie8

some online materials do say that a trapezoid must have "exactly" one pair of parallel sides |dw:1439129281970:dw|

29. 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.

30. 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.

31. ganeshie8

I remember facing issues with trapezoid and trapezium before haha

32. 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)

33. mathstudent55

@ganeshie8 As always, thanks for your insight.