Question

proving same - side interior angles supplementary. use the drop - down menus to complete the proof. given that w || x 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 definition of a linear pair. by the definition of supplementary angles, m∠3 + m∠1 = 180. substitute m∠5 for m∠1 to get m∠3 + m∠5 = 180. therefore, by the linear pair postulate and ∠3 and ∠5 are supplementary.

Explanation:

Step1: Identify angle - pair relationship

Given that \(m\angle3\) and \(m\angle1\) are a linear - pair. By the definition of a linear pair, they are supplementary.

Step2: Use corresponding angles property

Since \(w\parallel x\) and \(y\) is a transversal, \(\angle1\cong\angle5\) by the corresponding angles theorem. So \(m\angle1 = m\angle5\).

Step3: Substitute angle measures

Substitute \(m\angle5\) for \(m\angle1\) in \(m\angle3 + m\angle1=180^{\circ}\). We get \(m\angle3 + m\angle5 = 180^{\circ}\). Then, by the definition of supplementary angles, \(\angle3\) and \(\angle5\) are supplementary.

Answer:

The first blank is "definition of a linear pair", the second blank is "corresponding angles theorem", the third blank is "substitution property of equality".