Question

according to the given information, \\( \overline{uv} \\) is parallel to \\( \overline{wz} \\), while angles squ and vqt are vertical angles. angle vqt is congruent to angle squ by the vertical angles theorem. because angles squ and wrs are corresponding angles, they are congruent according to the corresponding angles theorem. finally, angle vqt is congruent to angle wrs by the ____ property. which property of equality accurately completes the proof? transitive subtraction substitution reflexive

Explanation:

Step1: Recall the Transitive Property

The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\). In this case, \(\angle VQT=\angle SQU\) (by Vertical Angles Theorem) and \(\angle SQU = \angle WRS\) (by Corresponding Angles Theorem). So, if we let \(a=\angle VQT\), \(b = \angle SQU\), and \(c=\angle WRS\), we can use the transitive property.

Step2: Eliminate other properties

• Subtraction Property: Deals with subtracting equal quantities from equal quantities (\(a=b\) implies \(a - c=b - c\)), which is not relevant here.
• Substitution Property: Replaces a variable with its value. But here we are establishing an equality between two angles based on two - step equalities (not just substitution of one value).
• Reflexive Property: States \(a=a\), which is not the case here.

Answer:

Transitive