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Section 5.5 Inequalities in One Triangle Theorem 5.10 • 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. 15 B 12 A A B THEOREM 5.11 • 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 60 o Side 2 Side 1 > Side 2 45 o Side 1 Write the sides/angles in order from least to greatest. A E 15 33 63 C 32 B F 22 D Is PQ>8? Is RQ<8? Q 57 61 P 8 R Exterior Angle Inequality • The measure of an exterior angle of a triangle is greater then the measure of either of the two nonadjacent interior angles. A 1 B <1 is greater than <A <1 is greater than <B What are the possible angle measures of <A? 42 A Triangle Inequality • The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A AB + BC >AC AC + BC > AB AB + AC > BC C B Is it possible to have a triangle with the given side lengths? • 3, 8, 3 • 6, 7, 12 • 9, 5, 11 • 8, 12, 20 What are the possible lengths of the third side of the triangle? • 8, 17, ? • 12, 18, ? Write and solve the inequality PQ + QR > PR. Q 2x+1 3x-3 P 3x+1 R