Question

given: x // y and w is a transversal. prove: ∠3 ≅ ∠6. what is the missing reason in the proof? statement reason 1. x // y, w is a transversal 1. given 2. ∠2 ≅ ∠3 2. def. of vert. ∠s 3. ∠2 ≅ ∠6 3. def. of corr. ∠s 4. ∠3 ≅ ∠6 4. transitive property symmetric property vertical angles are congruent definition of supplementary angles

Explanation:

Step1: Recall congruence properties

We know that if \(a = b\) and \(b = c\), then \(a=c\) by the transitive - property. Here, \(\angle3\cong\angle2\) (by definition of vertical angles) and \(\angle2\cong\angle6\) (by definition of corresponding angles).

Step2: Apply the property

Since \(\angle3\cong\angle2\) and \(\angle2\cong\angle6\), we can conclude that \(\angle3\cong\angle6\) using the transitive property of congruence.

Answer:

A. transitive property