Question

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

Answer 1

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 2

Option: B is the correct answer.

B. Rhombus; congruent adjacent sides property.

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.