Question

given: w || x and y is a transversal. prove: ∠3 and ∠5 are 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. 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. by the, m∠3 + m∠1 =. congruent supplements theorem, definition of a linear pair, definition of supplementary angles, linear pair postulate

Explanation:

Step1: Identify angle - congruence reason

Since \(w\parallel x\) and \(y\) is a transversal, \(\angle1\cong\angle5\) by the corresponding - angles postulate.

Step2: Identify linear - pair property

\(\angle3\) and \(\angle1\) are a linear pair. They are supplementary by the linear - pair postulate.

Step3: Substitute and conclude

By the substitution property, since \(m\angle1 = m\angle5\), we can substitute \(m\angle1\) with \(m\angle5\) in \(m\angle3 + m\angle1=180^{\circ}\) to get \(m\angle3 + m\angle5 = 180^{\circ}\), so \(\angle3\) and \(\angle5\) are supplementary by the definition of supplementary angles.

Answer:

1. corresponding - angles postulate
2. linear - pair postulate
3. substitution property