# Straight Line Drawn from the Vertex of a Triangle to the Base

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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