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Bronx High School of Science
Ms. Abbott
Mathematics Department
M$4
Unit 3: Indirect Proofs and Triangle Inequalities
DEFINITIONS
POSTULATES
 A whole is greater than any of its parts.
 If equal quantities are added to unequal quantities, then the sums are unequal in
the same order.
 If unequal quantities are added to unequal quantities of the same order, then the
sums are unequal in the same order.
 If equal quantities are subtracted from unequal quantities, then the differences are
unequal in the same order.
THEOREMS and COROLLARIES
 Triangle Inequality Theorem: In any triangle, the sum of the lengths of any two
sides is greater than the length of the third side.
 Exterior Angle Inequality Theorem: The measure of an exterior of a triangle is
greater than the measure of either of its remote interior angles.
 If the lengths of two sides of a triangle are unequal, then the measures of the
angles opposite the sides are unequal, and the greater angles lies opposite the
greater side.
 If the measures of two angles of a triangle are unequal, then the lengths of the
sides opposite the angles are unequal, and the greater side lies opposite the greater
angle.
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