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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