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Geometry 5.5 – Use Inequalities in a Triangle Learning Target: By the end of today’s lesson we will successfully be able to find possible side lengths of a triangle. 1) Mark the largest angle, longest side, smallest angle, and shortest side of the triangle shown below. What do you notice? The longest side and largest angle are _________________ each other. The shortest side and smallest angle are __________________ each other. 2) List the sides of ∆PQR in order from shortest to longest. THEOREM If one side of a triangle is longer than another side, then the angle opposite the longer side is _______________ than the angle opposite the shorter side. AB > BC, So m ____ > m _____. THEOREM If one angle of a triangle is larger than another angle, then the side opposite the larger angle is ______________ than the side opposite the smaller angle. m A > m C, So ______ >_______. 3) A long-tailed boat leaves a dock and travels 2500 feet to a cave, 5000 feet to a beach, then 6000 feet back to the dock as shown below. One of the angles in the path is about 55° and one is about 24°. What is the angle measure of the path made at the cave? TRIANGLE INEQUALITY THEOREM The sum of the lengths of any two sides of a triangle is greater than the length of the third side. 1) _______+ ______ > AC 2) AC + _____ > ______ 3) ______ + AC > ______ *** SHORTCUT*** If given 3 lengths and trying to determine if they could be a triangle, the SUM of the 2 SMALLEST sides must be GREATER than the third side. Determine if the following sets of numbers can be a triangle. Justify your answers! 4) 5, 8, 4 5) 16, 12, 28 6) 3, 4, 9 7) 11, 5, 8 *** If trying to find the possible length of a missing side of a triangle *** (difference of 2 given sides) < missing side < (sum of 2 given sides) 8) A triangle has one side of length 14 and another of length 10. Describe the possible lengths of the third side. 9) A triangle has one side of 23 meters and another of 17 meters. Describe the possible lengths of the third side.