Question

complete the proof with proof blocks or the 2 - column. given: m || n, ∠1≅∠3. prove: p || r. statements: 1. m || n 2. ∠1≅∠2 3. ∠1≅∠3 4. ∠2≅∠3 5. p || r reasons: 1. 2. 3. 4. 5.

Explanation:

Step1: Identify corresponding - angles

If \(m\parallel n\), then \(\angle1\cong\angle2\) by the corresponding - angles postulate.

Step2: Use transitive property

Given \(\angle1\cong\angle3\) and \(\angle1\cong\angle2\), by the transitive property of congruence, \(\angle2\cong\angle3\).

Step3: Prove parallel lines

Since \(\angle2\cong\angle3\), then \(p\parallel r\) by the converse of the corresponding - angles postulate.

Answer:

1. Given
2. Corresponding - angles postulate
3. Given
4. Transitive property of congruence
5. Converse of corresponding - angles postulate