Maths Exercises
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Maths Exercices

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:

Solution:

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:

Solution:

Look at the following picture:

We know that 67 + 53 + x = 180, that is, x = 60º.
Consequently NO, MN, MO