Question

1. given:

prove:
1.
2.
3.
4.
5.
6.

1. given:

Explanation:

Step1: Use the corresponding angles converse

If \(\angle1\cong\angle5\), then by the corresponding angles converse, \(t\parallel s\).

Step2: Use the alternate - interior angles

If \(\angle3\cong\angle4\), then by the alternate - interior angles converse, \(s\parallel v\).

Step3: Use the transitive property of parallel lines

Since \(t\parallel s\) and \(s\parallel v\), by the transitive property of parallel lines (if \(a\parallel b\) and \(b\parallel c\), then \(a\parallel c\)), we have \(t\parallel v\).

Answer:

The proof is completed as above to show \(t\parallel v\) using the corresponding angles converse, alternate - interior angles converse, and the transitive property of parallel lines.