Question

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

Explanation:

Step1: Recall linear - pair property

If two angles form a linear - pair, the sum of their measures is 180 degrees. In the given figure, $\angle1$ and $\angle2$ form a linear - pair. So, $m\angle1 + m\angle2=180^{\circ}$. The reason for this step is "Linear - pair postulate".

Step2: Use parallel - line properties

Since $x\parallel y$, corresponding angles are congruent. $\angle1$ and $\angle5$ are corresponding angles. By the corresponding - angles postulate, if two parallel lines are cut by a transversal, then corresponding angles are congruent. So, $\angle1\cong\angle5$.

Answer:

1. Linear - pair postulate; To prove $\angle1\cong\angle5$: Statements: 1) $x\parallel y$ (Given); 2) $m\angle1 + m\angle2 = 180^{\circ}$ (Linear - pair postulate); 3) $\angle1\cong\angle5$ (Corresponding - angles postulate)