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Euclidean Geometry

In PQR,D is...

Question

In $△ P Q R, D$ is the midpoint of side $Q R$ , seg $P D ⊥ s e g Q R$ . Then, can seg $P D$ be the altitude as well as the median of $△ P Q R$ ? Give resons for your answer ?

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Solution

Since the point $D$ is mid point of side $Q R$
It is the median of side $Q R$
Since the line $P D$ is $⊥$ of side $Q R$
It is the altitude of side $Q R$

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Q. 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.

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