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ABCD is a parallelogram and line CD = line DA. determine whether the parallelogram is a rhombus. if so by which property?
A. Rhombus; perpendicular diagonals property, B. Rhombus; congruent adjacent sides property, C. Rhombus; bisected angles property, D. Not a rhombus

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bcalle
Since it tells you it's a parallelogram you know that opposite sides are parallel.
The other piece of information we are given is a pair of consecutive congruent sides. If these sides are congruent the other sides must also be congruent.
Letter B is the answer

Answer:

Option: B is the correct answer.

    B.  Rhombus; congruent adjacent sides property.

Step-by-step explanation:

  • We know that a parallelogram is a quadrilateral which has two pair of parallel sides.
  • Also, a parallelogram will be called a rhombus if all the sides are of same length.
  • That is we may say that a Rhombus is a parallelogram but a parallelogram need not be a rhombus.

We are given that:

ABCD is a parallelogram ( this means AB||CD and BC||DA ) and line CD = line DA.

Hence,  the parallelogram is a rhombus by:

            Congruent adjacent sides property.

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