Question 23
Let $p$ be a line through the vertex $D$ of a given parallelogram $ABCD$, such that the vertices $A$, $B$ and $C$ are on the same side of $p$. Let $A'$, $B'$ and $C'$ be the bases of the altitudes from $A$, $B$ and $C$ to $p$ correspondingly. Prove that $\overline{BB'} = \overline{AA'} + \overline{CC'}$.