Here we will prove that any straight line drawn from the vertex of a triangle to the base is bisected by the straight line which joins the middle points of the other two sides of the triangle.
Solution:
Given: Q and R are the midpoints of the sides XY and XZ respectively of ∆PQR. P is any point on the base YZ. QR cuts XP at M.
To prove: QR bisects XP, i.e., XM = MP.
Proof:
Statement 
Reason 
1. QR ∥YZ. 
1. By the Midpoint Theorem. 
2. In ∆XYP, Q is the midpoint of XY and QM ∥ YP. 
2. From statement 1. 
3. QM bisects XP. 
3. By the converse of Midpoint Theorem. 
4. XM = MP. (Proved) 
4. From statement 3. 
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