Question

lines cut by a transversal proving same side interior angles supplementary given w || z and y is a transversal prove ∠3 and ∠5 are supplementary use the drop - down menus to complete the proof. given that w || z and y is a transversal we know that ∠1 ≅ ∠5 by the corresponding angles theorem therefore, m∠1 = m∠5 by the definition of congruent we also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the m∠3 + m∠1 = 180 now we can substitute m∠5 for m∠1 by the definition of supplementary angles, ∠3 and ∠5 a linear pair postulate congruent supplements theorem definition of a linear pair definition of supplementary angles

Explanation:

Step1: Recall corresponding - angles property

Given \(w\parallel z\) and \(y\) as a transversal, by the corresponding - angles theorem, \(\angle1\cong\angle5\), so \(m\angle1 = m\angle5\).

Step2: Recall linear - pair property

We know that, by definition, \(\angle3\) and \(\angle1\) are a linear pair. So, by the definition of supplementary angles, \(m\angle3 + m\angle1=180\).

Step3: Substitute and conclude

Now we can substitute \(m\angle5\) for \(m\angle1\) (since \(m\angle1 = m\angle5\)) into \(m\angle3 + m\angle1 = 180\). By the congruent - supplements theorem, \(\angle3\) and \(\angle5\) are supplementary.

Answer:

1. corresponding - angles theorem
2. definition of a linear pair
3. congruent - supplements theorem