Question

1. given: ∠1 ≅ ∠5, ∠3 ≅ ∠4

prove: l || v

Explanation:

Step1: State the given information

Given: $\angle1\cong\angle5$, $\angle3\cong\angle4$

Step2: Use the converse of corresponding angles postulate

Since $\angle1\cong\angle5$, by the converse of corresponding angles postulate, $r\parallel s$

Step3: Use the property of parallel lines

If $r\parallel s$, then $\angle2\cong\angle3$ (alternate interior angles)

Step4: Substitute using the given $\angle3\cong\angle4$

Since $\angle2\cong\angle3$ and $\angle3\cong\angle4$, then $\angle2\cong\angle4$

Step5: Use the converse of alternate interior angles theorem

By the converse of alternate interior angles theorem, if $\angle2\cong\angle4$, then $l\parallel v$

Answer:

1. $\angle1\cong\angle5$, $\angle3\cong\angle4$ - Given
2. $r\parallel s$ - Converse of corresponding angles postulate ($\angle1\cong\angle5$)
3. $\angle2\cong\angle3$ - Alternate interior angles ($r\parallel s$)
4. $\angle2\cong\angle4$ - Substitution ($\angle3\cong\angle4$ and $\angle2\cong\angle3$)
5. $l\parallel v$ - Converse of alternate interior angles theorem ($\angle2\cong\angle4$)