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Question
Math
Posted 2 months ago

Quadrilateral ABCDA B C D has the following vertices:
- A(6,8)A(6,8)
- B(6,5)B(6,-5)
- C(5,10)C(-5,-10)
- D(5,3)D(-5,3)

Is quadrilateral ABCDA B C D a rhombus, and why?
Choose 1 answer:
(A) Yes, because AB=BC=CD=ADA B=B C=C D=A D.
(B) Yes, because ABCD\overline{A B} \| \overline{C D}, and BCAD\overline{B C} \| \overline{A D}.
(C) No, because AB\overline{A B} is longer than BC\overline{B C}.
(D) No, because AB\overline{A B} is not parallel to BC\overline{B C}.
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
Using the asksia-ll calculator results, we find that AB=13AB = 13, BC=14612.083BC = \sqrt{146} \approx 12.083, CD=13CD = 13, and AD=14612.083AD = \sqrt{146} \approx 12.083
step 3
Since AB=CDAB = CD and BC=ADBC = AD, but ABBCAB \neq BC, the sides are not all equal
step 4
The asksia-ll calculator also confirms that lines ABAB and CDCD are parallel, as well as lines BCBC and ADAD
step 5
However, for a quadrilateral to be a rhombus, all four sides must be equal in length, which is not the case here
1 Answer
D
Key Concept
Properties of a Rhombus
Explanation
A rhombus is a quadrilateral with all sides equal in length. While ABCDABCD has opposite sides that are parallel, ABAB and BCBC are not equal, thus ABCDABCD is not a rhombus.

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