91Ó°ÊÓ

Prove that the supplement of an obtuse angle is an acute angle.

In triangle \(\mathrm{ABC}\), angles \(\mathrm{ABC}\) and \(\mathrm{ACB}\) are divided by \(\underline{\mathrm{BD}}\) and \(\underline{C E}\), respectively. This results in \(\mathrm{m} \angle \mathrm{BCE}>\mathrm{m} \angle \mathrm{DBC}\) and \(\mathrm{m} \angle \mathrm{ACE}>\mathrm{m} \angle \mathrm{ABD}\) Prove: \(\mathrm{m} \angle \mathrm{ACB}>\mathrm{m} \angle \mathrm{ABC}\).

Show that if two sides of a triangle are not congruent, then (1) the angles opposite these sides are not congruent, and (2) the angle with the greater measure is opposite the longer side.