Geometry

Question Analysis:
This question involves evaluating the logical validity of syllogisms.
The main focus is on determining whether the conclusion logically follows from the premises.

Key Concept Explanation:
A syllogism is valid if the conclusion necessarily follows from the premises. The premises must be true, and the logical structure must be correct.

Step-by-Step Solution:
Option A:
Premise 1: If a shape is a rhombus, then it is a parallelogram.
Premise 2: If a shape is a parallelogram, then it is a rectangle.
Conclusion: Therefore, all rhombuses are rectangles.
Analysis: This is invalid because not all parallelograms are rectangles (e.g., rhombuses are parallelograms but not necessarily rectangles).

Option B:
Premise 1: If a triangle is equilateral, then all its angles are equal.
Premise 2: If all angles in a triangle are equal, then each angle measures 60°.
Conclusion: Therefore, if a triangle is equilateral, each angle measures 60°.
Analysis: This is valid because the conclusion logically follows from the premises.
Equilateral triangles have equal angles, and in a triangle, equal angles must each be 60°.

Option C:
Premise 1: If a quadrilateral has four equal sides, then it is a rhombus.
Premise 2: If a quadril...