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 angles postulate 3) m∠5 + m∠8 = 180 3) linear pair theorem 4) blank 4) transitive property of equality

Explanation:

Step1: Analyze given equations

We have $m\angle3 + m\angle 8=180^{\circ}$ and $m\angle5 + m\angle8 = 180^{\circ}$.

Step2: Apply transitive - property of equality

If $a + c=b + c$, then $a = b$. Here, let $a=m\angle3$, $b = m\angle5$ and $c=m\angle8$. Since $m\angle3 + m\angle 8=m\angle5 + m\angle8$, we can conclude that $m\angle3=m\angle5$.

Answer:

$m\angle3=m\angle5$