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You are trying to prove that quadrilateral ABCD is a rhombus. You know that both pairs of opposite sides are parallel (a parallelogram). Which additional fact would prove that ABCD is a rhombus?

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ktreyb
Quadrilateral ABCD would be a rhombus if all sides of the quadrilateral are also equal in length. Also add on the fact that none of the angles are right angles. 

If all sides of ABCD parallelogram are equal then it becomes a rhombus.

What are the geometric properties of a parallelogram and a rhombus?

Parallelogram geometric properties

  1. Opposite sides are equal.
  2. Opposite angles are equal.
  3. Diagonal bisect each other.
  4. But diagonals are not equal in length.

Rhombus geometric properties

  1. All Sides are equal.
  2. Diagonals bisect at 90°.

In our question,

AB = DC is given for a quadrilateral ABCD (parallelogram).

Due to unequal sides of parallelogram, symmetry disturbed and their diagonals are not bisect at 90° but when its all sides are equal, then its diagonal bisect each other at 90° and it becomes a rhombus.

Hence a parallelogram is a rhombus when its all sides are equal.

To know more about geometric properties, refer to the link:

https://brainly.com/question/15996204

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