Question

complete the two - column proof. given: x||y prove: ∠3≅∠5. statements: 1) x||y; 2) m∠3 + m∠5 = 180

Explanation:

Step1: Given parallel lines

We are given \(x\parallel y\). By the Same - Side Interior Angle Postulate, when two parallel lines are cut by a transversal, same - side interior angles are supplementary. So, if \(\angle3\) and \(\angle5\) are same - side interior angles, \(m\angle3 + m\angle5=180\).

Step2: Justify the second statement

The reason for \(m\angle3 + m\angle5 = 180\) is the Same - Side Interior Angle Postulate.

Answer:

The reason for statement 2 (\(m\angle3 + m\angle5 = 180\)) should be "Same - Side Interior Angle Postulate" instead of "Transitive Property of Equality".