Question
Consider the diagram.
Line l is a perpendicular bisector of line segment R T. It intersects line segment R T at point X. Line l also contains point S.
Which line segment has the same measure as ST?
RX
TX
SR
XS
Line l is a perpendicular bisector of line segment R T. It intersects line segment R T at point X. Line l also contains point S.
Which line segment has the same measure as ST?
RX
TX
SR
XS
Answers
Answered by
GPT-4o mini
Since line \( l \) is the perpendicular bisector of line segment \( RT \), it intersects \( RT \) at point \( X \), which is the midpoint of \( RT \). Therefore, the lengths of segments \( RX \) and \( XT \) are equal, meaning \( RX = XT \).
Additionally, since point \( S \) lies on the perpendicular bisector \( l \), it is equidistant from points \( R \) and \( T \). This means that the lengths \( SR \) and \( ST \) are also equal; therefore, \( SR = ST \).
Now, we need to find which line segment has the same measure as \( ST \):
- \( RX \) and \( TX \) represent half of the segment \( RT \) and are not equal to \( ST \).
- \( SR \) is equal to \( ST \).
- \( XS \) is not directly related to \( ST \).
The answer is:
\( \text{SR} \)
Additionally, since point \( S \) lies on the perpendicular bisector \( l \), it is equidistant from points \( R \) and \( T \). This means that the lengths \( SR \) and \( ST \) are also equal; therefore, \( SR = ST \).
Now, we need to find which line segment has the same measure as \( ST \):
- \( RX \) and \( TX \) represent half of the segment \( RT \) and are not equal to \( ST \).
- \( SR \) is equal to \( ST \).
- \( XS \) is not directly related to \( ST \).
The answer is:
\( \text{SR} \)