__Definition of Inequality__ - for any real numbers a and b, a > b if and only
if there is a positive number c such that a = b + c

__Exterior Angle Inequality Theorem__ - if an angle is an exterior angle of a triangle,
then its measure is greater than the measure of either of its
corresponding remote interior angles

__Theorem__ - if
one side of a triangle is longer than another side, then the angle
opposite the longer side has a greater measure than the angle
opposite the shorter side

__Theorem__ - If
one angle of a triangle has a greater measure than another angle,
then the side opposite the greater angle is longer than the side
opposite the lesser angle

__Theorem__ - The
perpendicular segment from a point to a line is the shortest segmennt
from the point to that line

__Triangle Inequality Theorem__ - the sum of the lengths of any two sides of a triangle
is greater than the lengths of the third side

__SAS Inequality Theorem__
- if two sides of one triangle are congruent to two sides of another
triangle and the included angle in one triangle has a greater
measure than the included angle in the other, then the third side
of the first triangle is longer than the third side of the second
triangle

__SSS Inequality Theorem__
- if two sides of one triangle are congruent to two sides of another
triangle and the third side in one triangle is longer than the
third side in the other, then the angle between the pair of congruent
sides in the first triangle is greater than the corresponding
angle un the second triangle

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