complete the proof that ( overleftrightarrow{uw} parallel overleftrightarrow{rt} ).
complete the proof that ( overleftrightarrow{uw} parallel overleftrightarrow{rt} ).
Answer
Explanation:
Step1: Recall the Transitive Property of Parallel Lines
If (a\parallel b) and (b\parallel c), then (a\parallel c).
Step2: Apply the Transitive Property
We are given (\overleftrightarrow{FH}\parallel\overleftrightarrow{UW}) (Statement 1) and (\overleftrightarrow{RT}\parallel\overleftrightarrow{FH}) (Statement 2). Let (a = \overleftrightarrow{UW}), (b=\overleftrightarrow{FH}), (c = \overleftrightarrow{RT}). By the Transitive Property of Parallel Lines (if two lines are parallel to the same line, then they are parallel to each other), since (\overleftrightarrow{UW}\parallel\overleftrightarrow{FH}) and (\overleftrightarrow{RT}\parallel\overleftrightarrow{FH}), we can conclude (\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}).
Answer:
The reason for Statement 6 ((\overleftrightarrow{UW}\parallel\overleftrightarrow{RT})) is the Transitive Property of Parallel Lines.