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Geometry Lesson 5.3.notebook January 05, 2015 Inequalities in One Triangle Comparison Property of Inequality or Transitive Property of Inequality If and then If and then Addition Property of Inequality If then If then Subtraction Property of Inequality If then If then By the Exterior Angle Theorem, we know that Because the angles must be positive, we know that 1 Geometry Lesson 5.3.notebook January 05, 2015 The Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater then the measure of either of its corresponding remote interior angles. Using the Exterior angle Inequality Theorem, list all the angles that satisfy the stated condition. (Do not go by what the angles look like, only by what can be determined by the theorem!!!) a. measures less than b. measures greater than 2 Geometry Lesson 5.3.notebook January 05, 2015 Angle Side Relationships in Triangles Theorem If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. If AC > BC, then Theorem If one angle of a triangle is greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. If then AB > BC. List the angles of from smallest to largest. 3 Geometry Lesson 5.3.notebook January 05, 2015 List the sides of in order from shortest to longest. 4 Geometry Lesson 5.3.notebook January 05, 2015 Tim and Teresa are lifeguards at the pool. While they are working a swimmer begins to go into distress. Using the figure below, If Tim is LG1 and Teresa is LG2, who is closest to the swimmer? 5 Geometry Lesson 5.3.notebook January 05, 2015 Page 346 838, 41 6