Question

given:
p: angles xyz and rst are vertical angles.
q: angles xyz and rst are congruent.
which statement is logically equivalent to ( p \to q )?
if angles xyz and rst are congruent, then they are vertical angles.
if angles xyz and rst are not vertical angles, then they are not congruent.
if angles xyz and rst are not congruent, then they are not vertical angles.
if angles xyz and rst are vertical angles, then they are not congruent.

Explanation:

Step1: Recall the contrapositive rule

The contrapositive of \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\).

Step2: Substitute \(p\) and \(q\)

Given \(p\): Angles \(XYZ\) and \(RST\) are vertical angles. \(
eg p\): Angles \(XYZ\) and \(RST\) are not vertical angles.
Given \(q\): Angles \(XYZ\) and \(RST\) are congruent. \(
eg q\): Angles \(XYZ\) and \(RST\) are not congruent.
The contrapositive \(
eg q
ightarrow
eg p\) is "If angles \(XYZ\) and \(RST\) are not congruent, then they are not vertical angles".

Answer:

If angles \(XYZ\) and \(RST\) are not congruent, then they are not vertical angles.