To show that 4 points are the vertices of a rhombus, which of the following must be shown? a. all sides are of equal length. b. the diagonals are of equal length. c. the opposite sides are of equal length and the diagonals are of equal length. d. the opposite sides are parallel and the diagonals are of equal length.

A)

Step-by-step explanation:

The starting point to solve this, is to gather the concept of what a Rhombus is, an Equilateral Parallelogram, so let's examine the following options

A. All sides are of equal length. True

Considering the definition hence all sides have the same length.

B. The Diagonals are of equal length False. Since there is a bigger diagonal than the second Diagonal, we cannot assure they're of equal lengths.

Check the picture out below

C. The opposite sides are of equal length and the diagonals are of equal length False. Since those diagonals are different we cannot agree with the second part

D. The opposite sides are parallel and the diagonals are of equal length False Different length for each diagonal.

By definition of rhombus, we know that rhombus is any parallelogram with equal sides. Means the only requirement is to get all sides equal.

Hence choice "A. All sides are of equal length. " is correct

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