Geometry

Question Analysis:
This question involves identifying a logical fallacy in syllogisms.
The main focus is on determining whether the conclusion logically follows from the premises.

Key Concept Explanation:
A logical fallacy occurs when the conclusion does not logically follow from the premises, or when the premises are irrelevant or contradictory.

Step-by-Step Solution:
Option A:
Premise 1: All parallelograms have opposite sides that are congruent.
Premise 2: A rhombus is a parallelogram.
Conclusion: Therefore, a rhombus has opposite sides that are congruent.
Analysis: This is valid because the conclusion logically follows from the premises.
Rhombuses are parallelograms, so they inherit the property of having congruent opposite sides.

Option B:
Premise 1: All squares have four congruent sides.
Premise 2: A rectangle has four right angles.
Conclusion: Therefore, all rectangles have four congruent sides.
Analysis: This is invalid because the premises do not logically lead to the conclusion.
Rectangles do not necessarily have four congruent sides (only squares do).
This commits a non sequitur fallacy (the conclusion does not follow from the premises).

Option C:
Premise 1: If a quadrilateral is a square, then it has four right angles.
Premise 2: If a quadrilateral has four right angles...