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Equidistant Angle Bisector Theorem: P is on the bisector of ∠ABC, if and only if P is equidistant to each side, AP = PC. Perpendicular Bisector Theorem: P is on the⊥ bisector of AB if and only if P is equidistant to A & B. AP = PB l A M A P D B P B INEQUALITIES IN ONE ∆ Exterior Angle Inequality m∠4 > m∠1 & m∠4 > m∠2 1 2 3 C ∆ Inequality a+b>c b+c>a c+a>b ⇓ |a - b| < c < a + b c a B Opposites Inequality m∠A > m∠B > m∠C ⇔ BC > CA > AB The larger angles are opposite the larger sides in a ∆. T INEQUALITIES IN TWO ∆’s C Y Z 4 A b B C Triangle Midsegment Theorem If IM = MT & ID = DR, I then ① MD = 1 TR. M D 2 ➁ MD//TR. R A X SAS ∆ Inequality If AB = XY and AC = XZ and m∠A < m∠X, then BC < YZ. SSS ∆ Inequality If AB = XY and AC = XZ and BC < YZ, then m∠A < m∠X. Midsegment Corollary The joined midpoints of consecutive sides of any quadrilateral form a parallelogram.