Quadrilateral ABCD has diagonals AC and BDWhich information is not sufficient to prove and ABCD is a parallelogram?Group of answer choicesAB is congruent to CD and BC is congruent to ADAB is congruent to CD and AB is parallel to CDAB is congruent to CD and BC is parallel to ADAC and BD bisect each other
Question
Quadrilateral ABCD has diagonals AC and BDWhich information is not sufficient to prove and ABCD is a parallelogram?Group of answer choicesAB is congruent to CD and BC is congruent to ADAB is congruent to CD and AB is parallel to CDAB is congruent to CD and BC is parallel to ADAC and BD bisect each other
Solution
The information "AB is congruent to CD and AB is parallel to CD" is not sufficient to prove that ABCD is a parallelogram.
In a parallelogram, opposite sides are equal (AB = CD and BC = AD) and opposite sides are parallel (AB || CD and BC || AD). However, the statement "AB is congruent to CD and AB is parallel to CD" only provides one pair of equal and parallel sides. It does not provide information about the other pair of sides, which is necessary to prove that a quadrilateral is a parallelogram.
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