Angle Side Theorem – Inequalities in One Triangle
“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.”
Sample Problem 1:
Write the angles in order from smallest to largest
Converse of Angle Side Theorem – Inequalities in One Triangle
“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.”
Sample Problem 2:
Write the sides in order from shortest to longest.
Exterior Angle Inequality Theorem
“The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.”
Sample Problem 3:
Determine the smallest and the largest angles.
Triangle Inequality Theorem
“The sum of the lengths of any two sides of a triangle is greater than the length of the third side.”
Sample Problem 4:
A triangle has one side of length 12 and another of length 8. Identify the possible lengths of the third side.
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