Question

In ∆PQR, D is the mid-point of side QR. Seg PD ⊥ seg QR. Then, can seg PD be the altitude as well as the median of ∆PQR? Give reasons for your answer.

Answer 1

An altitude of a triangle is the perpendicular drawn from a vertex to the opposite side of the triangle.
It is given that PD ⊥ seg QR.
∴ PD is an altitude of the ∆PQR … (1)
The line segment joining any vertex of a triangle to the mid-point of its opposite side is called the median of the triangle.
It is given that D is the mid-point of seg QR.
∴ PD is a median of the ∆PQR … (2)
∴ PD is both an altitude and a median. (From 1 and 2)
So, we can say that PD can be the altitude as well as the median of ∆PQR.