Triangle Side and Angle Inequalities
Side Inequality Theorem: If one side of a triangle is longer than the other side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
If AC>BC>AB, then m<B > m<A > m<C
List the angles in order of smallest to largest:
m<S, m<R, m<Q
Angle Inequality Theorem: If one angle of a triagle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
If m<A > m<B > m<C, then BC>AC>AB
List the sides in order of longest to shortest:
Look at the following picture:
We know that 67 + 53 + x = 180, that is, x = 60º.
Consequently NO, MN, MO