Final Answer:
If n ∥ p and pm, then b) nₚ
Step-by-step explanation:
When given that n ∥ p and pm, it implies that n is parallel to p and p is parallel to m. Therefore, by the transitive property of parallel lines, n is also parallel to m. The correct completion of the statement is b) nₚ, indicating that n is parallel to both p and m.
In geometry, the parallel line transitive property states that if one line is parallel to a second line, and the second line is parallel to a third line, then the first line is parallel to the third line. In this scenario, n is parallel to p and p is parallel to m, so n must be parallel to m as well. Therefore, the correct completion of the statement is b) nₚ, signifying that n is parallel to both p and m.
In summary, the relationship n ∥ p and pm implies that n is parallel to both p and m, making the correct answer b) nₚ. This aligns with the transitive property of parallel lines in geometry.