Geometry

Question Analysis:
This question involves identifying a logically valid syllogism in geometric reasoning.
The main focus is on determining which statement follows a proper deductive structure.

Key Concept Explanation:
A syllogism is a form of deductive reasoning that consists of:
A major premise (a general statement)
A minor premise (a specific statement that connects to the major premise)
A conclusion (a logical result that follows from both premises)
A valid syllogism follows this pattern:
If P → Q (Major Premise)
If Q → R (Minor Premise)
Then P → R (Conclusion)

Step-by-Step Solution:
Now, let’s analyze each option for logical validity.

A) If two lines are perpendicular, they form right angles. If an angle is a right angle, it measures 90 degrees. Therefore, perpendicular lines form 90-degree angles.
Major Premise: If two lines are perpendicular, they form right angles. (P → Q)
Minor Premise: If an angle is a right angle, it measures 90 degrees. (Q → R)
Conclusion: Perpendicular lines form 90-degree angles. (P → R)
✅ This follows the correct logical structure and is the correct answer.

B) If two triangles are congruent, their corresponding sides are equal. If two sides are equal, the triangles are similar. Therefore, all congruent triangles are similar.
Major Premise: If two triangles are congruent, their corresponding sides are equal. (P → Q)
Minor Premise: If two sides are equal, the triangles are similar. (Q → R)
Incorrect Conclusion: "All congruent triangles are similar."
This is incorrect because congruence implies equal angles and equal sides, but similarity only requires proportional sides and equal angles.
Not all congruent triangles are just similar; they are also identical.
❌ Invalid syllogism due to a flawed conclusion.

C) If a quadrilateral is a rectangle, it has four equal sides. If it has four equal sides, it is a square. Therefore, all rectangl...