Question

1. given: ∠1≅∠5,∠3≅∠4 prove: l || v statements reasons ∠1≅∠5 ∠3≅∠4 ∠3 = ∠5 ∠4 = ∠3 ∠4 = ∠5 l || v given given

Explanation:

Step1: State the given angles

Given $\angle1\cong\angle5$ and $\angle3\cong\angle4$.

Step2: Use the property of vertical - angles

Vertical angles are congruent. $\angle1$ and $\angle2$ are vertical angles, so $\angle1 = \angle2$. Since $\angle1\cong\angle5$, then $\angle2\cong\angle5$ (by the transitive property of congruence).

Step3: Recall the corresponding - angles postulate

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. $\angle2$ and $\angle5$ are corresponding angles. Since $\angle2\cong\angle5$, we can conclude that $l\parallel v$.

Answer:

The proof that $l\parallel v$ is completed by using the given angle - congruences, the property of vertical angles, and the corresponding - angles postulate.