## Elementary Geometry for College Students (6th Edition)

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.