Here we will prove that in the given ∆XYZ, M and N are the midpoints of XY and XZ respectively. T is any point on the base YZ. Prove that MN bisects XT.
Solution:
Given: In ∆XYZ, XM = MY and XN = NZ. MN cuts XT at U.
To prove: XU = UT.
Construction: Through X, draw PQ ∥ YZ.
Proof:
Statement 
Reason 
1. MN ∥ YZ. 
1. The line segment joining the midpoints of the two sides of a triangle is parallel to the third side. 
2. PQ ∥ MN ∥ YZ. 
2. PQ ∥ YZ and MN ∥ YZ. 
3. The transversal XY makes equal intercepts on PQ, MN and YZ. 
3. Given that XM = MY. 
4. The transversal XT also makes equal intercepts on PQ, MN and YZ. 
4. By the Equal Intercepts Theorem. 
5. XU = UT. (Proved) 
5. From statement 4. 
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