High School

We appreciate your visit to The diagonals of quadrilateral WXYZ intersect at R If R is the midpoint of WY and XZ which additional statement shows that WXYZ is a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The diagonals of quadrilateral WXYZ intersect at R. If R is the midpoint of WY and XZ, which additional statement shows that WXYZ is a square?

1. WY ≌ XZ
2. ∠WZY = 90°
3. WY ⊥ XZ
4. A and C

A. A
B. B
C. C
D. D

Answer :

Final answer:

To confirm that WXYZ is a square given that R is the midpoint of both diagonals, the additional information needed is that the diagonals are congruent and perpendicular. The correct choice is d: Options 1 and 3.

Explanation:

To determine if quadrilateral WXYZ is a square, we can analyze the given options. For a quadrilateral to be a square, it must have equal sides, equal diagonals, and all angles must be 90 degrees.

  • Option 1: WY ≅ XZ. If both diagonals are congruent, it supports the idea of a square, but it is not sufficient alone since rhombuses also have this property.
  • Option 2: ∠ WZY=90°. A single 90-degree angle does not ensure all angles are 90 degrees and that sides are equal.
  • Option 3: WY⊥XZ. If the diagonals are perpendicular, this suggests a square or a rhombus, but, like option 1, alone it is not enough.
  • Options 1 and 3: WY ≅ XZ and WY⊥XZ. When the diagonals are both congruent and perpendicular, it indicates a square because a rhombus would not necessarily have congruent diagonals.

Therefore, given that R is the midpoint of both diagonals (WY and XZ), the additional information needed to conclude that WXYZ is a square is that both diagonals are congruent and perpendicular to each other. So, the correct option is d: Choices 1 and 3.

Thanks for taking the time to read The diagonals of quadrilateral WXYZ intersect at R If R is the midpoint of WY and XZ which additional statement shows that WXYZ is a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada