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anonymous

  • one year ago

Quadrilateral ABC has opposite sides that are parallel and side AB congruent to side DC. What classification can be given to ABCD

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  1. mathstudent55
    • one year ago
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    |dw:1439479120097:dw|

  2. mathstudent55
    • one year ago
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    Both pairs of opposite sides are parallel. There is a quadrilateral whose definition is exactly that. Do you know which quadrilateral that is?

  3. anonymous
    • one year ago
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    Parallelogram

  4. mathstudent55
    • one year ago
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    Correct. From the two pairs of parallel opposite sides, we know it's a parallelogram. Now let's look at the second piece of information. Sides AB and DC are congruent. |dw:1439479386915:dw|

  5. mathstudent55
    • one year ago
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    In a parallelogram, opposite sides are congruent. This information does not add anything to what we already knew, so the conclusion is that polygon ABCD is a parallelogram.

  6. anonymous
    • one year ago
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    Thanks for your help

  7. mathstudent55
    • one year ago
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    If two adjacent sides were congruent, such as sides AB and BC, then all sides would be congruent, and we would be able to conclude it's a rhombus. This is not the case, so all we know is it's a parallelogram.

  8. mathstudent55
    • one year ago
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    You're welcome.

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