Here we will prove that converse of the Midpoint Theorem by using the Equal Intercepts Theorem.
Solution:
Given: P is the midpoint of XY in ∆XYZ. PQ ∥ YZ.
To prove: XQ = QZ.
Construction: Through X, draw MN ∥ YZ.
Proof:
Statement 
Reason 
1. PQ ∥ YZ. 
1. MN ∥ YZ and PQ ∥ YZ. 
2. MN ∥ PQ ∥ YZ. 
2. XP = PY. 
3. The transversal XZ also makes equal intercepts XQ and QZ on MN, PQ and YZ. 
3. By the Equal Intercepts Theorem. 
4. Therefore, XQ = QZ. (Proved) 
4. From statement 3. 
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