Question

complete the two - column proof. given: x||y prove: ∠3≅∠5 1) x||y 1) given 2) m∠3 + m∠8 = 180 2) same - side interior angle postulate 3) m∠5 + m∠8 = 180 3) linear pair theorem 4) 4) transitive property of equality

Explanation:

Step1: Recall given and previous steps

We know from step 2 that $m\angle3 + m\angle8=180$ and from step 3 that $m\angle5 + m\angle8 = 180$.

Step2: Apply transitive property

Since $m\angle3 + m\angle8=m\angle5 + m\angle8 = 180$, by the transitive property of equality, we can conclude that $m\angle3=m\angle5$.

Step3: Convert to congruence

If two angles have equal measures, they are congruent. So $\angle3\cong\angle5$.

Answer:

$m\angle3 = m\angle5$ (or $\angle3\cong\angle5$)