The straight line drawn through the midpoint of one side of a triangle parallel to another bisects the third side.
Given: In ∆PQR, S is the midpoint of PQ, and ST is drawn parallel to QR.
To prove: ST bisects PR, i.e., PT = TR.
Construction: Join SU where U is the midpoint of PR.
Proof:
Statement 
Reason 
1. SU ∥ QR and SU = \(\frac{1}{2}\)QR. 
1. By Midpoint Theorem. 
2. ST ∥QR and SU ∥ QR. 
2. Given and statement 1. 
3. ST ∥ SU. 
3. Two lines parallel to the same line are parallel themselves. 
4. ST and SU are not the same line. 
4. From statement 3. 
5. T and U are coincident points. 
5. From statement 4. 
6. T is the midpoint of PR (Proved). 
6. From statement 5. 
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