Answer
The altitudes to and to are congruent. This is because QMN and QPN are congruent; corresponding altitudes of congruent triangles are congruent.
Work Step by Step
Draw an altitude from Q on PN at R
Draw an altitude from Q on MN at O
Let us take altitude $\overline{QR}$ and $\overline{QO}$
Lets compare $\triangle$ QMN and $\triangle$ QPN
$\overline{QM}$ = $\overline{PN}$
$\overline{MN}$ = $\overline{PQ}$
$\overline{QN}$ = $\overline{QN}$ (common)
By SSS property $\triangle$ QMN and $\triangle$ QPN are congruent
Therefore the altitudes to $\overline{PN}$ and $\overline{MN}$ are congruent $\overline{QO}$ and $\overline{QR}$ because we know corresponding altitudes of congruent triangles are equal.
