Geometry

Question Analysis:
This question involves applying the Law of Syllogism and the Law of Detachment to draw a valid conclusion from the given statements.
The main focus is on understanding the logical relationships between the statements and identifying which conclusion must be true.

Key Concept Explanation:
Law of Syllogism:
If "If P, then Q" and "If Q, then R" are both true, then "If P, then R" is also true.
Law of Detachment:
If "If P, then Q" is true, and P is true, then Q must be true.

Step-by-Step Solution:
Apply the Law of Syllogism:
From Statement 1 and Statement 2, we can conclude:
"If a quadrilateral has four congruent sides and four right angles, then its diagonals are congruent."
This is because "If P, then Q" and "If Q, then R" together imply "If P, then R."

Apply the Law of Detachment:
Since PQRS has four congruent sides and four right angles (P is true), and we have "If P, then R," we can conclude:
"The diagonals of PQRS are congruent."

Evaluate the Options:
A) The diagonals of PQRS are congruent.
This is true based on the conclusion above.
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