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.

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

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.







9th Grade Math

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