Question

try it! 2. theorem 2-10 states that through a point not on a line, there is one and only one line parallel to the given line. how does this justify the construction of the line through c that is parallel to the line ab? enter your answer.

Explanation:

Point \( C \) is not on line \( \overleftrightarrow{AB} \). By Theorem 2 - 10, there is exactly one line through \( C \) parallel to \( \overleftrightarrow{AB} \). The construction (e.g., using angle - copying methods like making \( \angle 4=\angle 1 \) or \( \angle 5 = \angle 2 \)) results in a line through \( C \). The theorem justifies that this constructed line is the only one parallel to \( \overleftrightarrow{AB} \) through \( C \), so the construction is valid as it creates the unique parallel line guaranteed by the theorem.

Answer:

Point \( C \) is not on \( \overleftrightarrow{AB} \). Theorem 2 - 10 says there's exactly one line through \( C \) parallel to \( \overleftrightarrow{AB} \). The construction (e.g., angle - copying) creates this unique parallel line, so the theorem justifies the construction as it guarantees only one such line exists through \( C \).