A line segment is a given line that does not have endpoints. The required statements and reasons for the proof are stated below:
A line segment is a given line that does not have endpoints. It consists of a series of interconnected points in a straight line.
Considering segment SW with points S, T, U, V, W, the following proofs can be deduced:
STATEMENT REASON
U is the midpoint of SW Given
T is the midpoint of SU Given
V is the midpoint of UW Given
SW = SU + UW Definition of a midpoint
SU = ST + TU Definition of a midpoint
UW + UV + VW Definition of a midpoint
ST = TU Equal parts of a line segment
UV = VW Equal parts of a line segment
TV = TU + UV Definition of a midpoint
Therefore,
TU ≅ UV Midpoint property of a line segment
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