Question

complete the two - column proof. given: x||y prove: ∠3≅∠5 2) m∠3 + m∠8 = 180 2) same - side interior angle postulate 3) m∠5 + m∠8 = 180 3) linear pair theorem 4) m∠3 + m∠8 = m∠5 + m∠8 4) transitive property of equality 5) 5) subtraction property of equality

Explanation:

Step1: State given equal - angle sums

We know that \(m\angle3 + m\angle8=m\angle5 + m\angle8\) from the transitive property.

Step2: Apply subtraction property

Subtract \(m\angle8\) from both sides of the equation \(m\angle3 + m\angle8=m\angle5 + m\angle8\).
\[m\angle3 + m\angle8 - m\angle8=m\angle5 + m\angle8 - m\angle8\]
\[m\angle3=m\angle5\]
Since \(m\angle3=m\angle5\), then \(\angle3\cong\angle5\) (angles with equal measures are congruent).

Answer:

\(m\angle3 = m\angle5\) (so \(\angle3\cong\angle5\))