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Question 4 • **MFISD GEOMETRY A 22-23 CR

Given:p: Angles XYZ and RST are vertical angles.q: Angles XYZ and RST are congruent.Which statement is logically equivalent to p → q?

Answer
A
If angles XYZ and RST are congruent, then they are vertical angles.
B
If angles XYZ and RST are not vertical angles, then they are not congruent.
C
If angles XYZ and RST are not congruent, then they are not vertical angles.
D
If angles XYZ and RST are vertical angles, then they are not congruent.

Explanation

A conditional statement p → q is logically equivalent to its contrapositive, not q → not p. Here, q says the angles are congruent, so not q means they are not congruent; not p means they are not vertical angles. Therefore, choice C, “If the angles are not congruent, then they are not vertical angles,” is equivalent.

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