Question

The question is in the picture of possible write in a two column proof or something similar

Answer 1

The theorem we want to prove says that:

Two lines that are parallel to a third line are parallel.

Statement 1:

n || m and p || m

Reason 1:

Given

Statement 2:

`\angle1\cong\angle2\, and\, \angle1\cong\angle3`

Reason 2:

The pairs are corresponding angles

Statement 3:

`\angle2\cong\angle3`

Reason 3:

Transitive property of congruency, that is:

`\begin{gathered} if \\ \angle1\cong\angle2\, and\, \angle1\cong\angle3 \\ then \\ \angle2\cong\angle3 \end{gathered}`

Statement 4:

`\angle2\, and\, \angle3\, are\, corresponding\, angles`

Reason 4:

If the angles formed between a line and two other lines are equal, they are corresponding angles.

Statement 5:

n || p

Reason 5:

If two angles are corresponding angles, the lines that form them are parallel (this is the backwards of the reason 2).