Question

given: m || n, n || q
prove: m || q

1. click here to insert
2. transitive property
3. m || q
4. click here to insert

Explanation:

Step1: Identify given parallel lines

We are given $m\parallel n$ and $n\parallel q$. These are the statements used for the transitive - property application.

Step2: State the conclusion

Based on the transitive property of parallel lines (if line $a$ is parallel to line $b$ and line $b$ is parallel to line $c$, then line $a$ is parallel to line $c$), we conclude that $m\parallel q$. The reason for stating $m\parallel q$ is the application of this well - known geometric property.

Answer:

1. $m\parallel n,n\parallel q$
2. Definition of congruence (or the fact that if two lines are parallel to the same line, they are parallel to each other which is based on the transitive - like property in parallel - line geometry)