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The diagonals of quadrilateral WXYZ intersect at R. If R is the midpoint of WY and XZ, and WR = XR, what is the most specific quadrilateral that WXYZ can be?

A. rhombus
B. square
C. rectangle
D. parallelogram

Answer :

Final answer:

The most specific quadrilateral in this case is a rhombus. This is because in a rhombus, the diagonals intersect at a right angle, are of equal length, and bisect each other. Moreover, the condition WR = XR indicates equal bisected lengths which is specific to a rhombus.

Explanation:

The most specific quadrilateral that WXYZ can be is a rhombus. This is because in a rhombus, the diagonals intersect at a right angle and are also of equal length. They bisect each other, making the point of intersection (R in this case) the midpoint of both diagonals (WY and XZ). Furthermore, the given condition that WR = XR adds to the argument that the quadrilateral is a rhombus as this implies that the diagonals are not only bisected but also that these bisected lengths are equal which is specific to a rhombus and not necessarily true for a parallelogram, rectangle or square.

Learn more about Rhombus here:

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