Geometry

Question Analysis:
This question involves identifying an invalid deductive reasoning step.
The main focus is on recognizing when a deductive argument fails to guarantee the truth of its conclusion, even if the premises are true.

Key Concept Explanation:
A valid deductive argument follows the structure:
If P, then Q. (General rule)
P is true. (Specific case)
Therefore, Q is true. (Conclusion)
An invalid deductive argument occurs when the conclusion does not logically follow from the premises, even if the premises are true.

Step-by-Step Solution:
Analyze each option to determine if it represents a valid or invalid deductive reasoning step:
A) This is a valid deductive argument because:
Premise 1: If a number is even, then it is divisible by 2. (General rule)
Premise 2: 4 is even. (Specific case)
Conclusion: Therefore, 4 is divisible by 2. (Logically certain)
B) This is an invalid deductive argument because:
Premise 1: If a polygon is a pentagon, then it has five sides. (General rule)
Premise 2: A shape has five sides. (Specific case)
Conclusion: Therefore, it must be a pentagon. (Not logically certain)
The argument is invalid because having five sides does not guarantee that the shape is a pentagon.
Other shapes (e.g., irregular polygons) can also have five sides.
C) This is a valid deductive argument because:
Premise 1: If an angle is 90 degrees, then it is a right angle. (General...