Geometry chapter 5.5 Inequalities in One Triangle
I) Theorems:
A) If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
B) If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
C) Exterior Angle Inequality - the measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles.
Example: Given ΔABC with side BC extended to point D forming exterior angle ACD,
measure of angle ACD > measure of angle A and
measure of angle ACD > measure of angle B
D) Triangle Inequality - the sum of the lengths of any two sides of a triangle is great than the length of the third side.
Example: Given the triangle has lengths of 5 and 15, what is the other length x?
5 + 15 = 20 and 15 - 5 = 10, therefore the third length is
10 < x < 20
