Question

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 1

When two lines intersect they form a figure similar to an X, where there are 4 angles, those that are opposite to each other are called vertical angles. These vertical angles are congruent as can be seen in the attached figure.

Where:

$\beta =\mu$

$\alpha = \theta$

Therefore, the statement that is logically equivalent to p → q is:

If the angles XYZ and RST are vertical angles, then the angles XYZ and RST are congruent

In the same way, if the angles XYZ and RST are not congruent, then the angles XYZ and RST are not vertical. (Because all vertical angles are congruent)

¬q → ¬p