Chapter 6.5, Problem 46HP

To determine

To explain:

The name of person who gives the correct statement about the quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$

Answer to Problem 46HP

Both are incorrect. The given quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is only categorized as rectangle since they don’t know the sides are congruent or not.

Explanation of Solution

Given information:

  

Know that:

According to Lola: The quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is a square

According to Xavier: The quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is a rhombus

In the given figure of quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ :

  $\overline{\mathrm{P}\mathrm{R}}\cong \overline{\mathrm{Q}\mathrm{S}}$

Both are not correct because the given information only says that the quadrilateral has congruent diagonals which not clearly defines is as wither rhombus or square.

To define the given quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ as square or rhombus, there is need angles information and side’s information of quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ which should be congruent.

Thus, the judgments passed by Lola and Xavier are not correct. The given quadrilateral $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is only categorized as rectangle since they don’t know the sides are congruent or not.