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Warm-Up Bell WorkExercises - Matching A) Circumcenter B) Incenter C) Centroid D) Orthocenter 1) Medians 2) Perpendicular Bisectors 3) Angle Bisectors 4) Altitudes a) Equidistant from sides b) Equidistant from vertices c) Distance to vertices is 2/3 of the distance from the vertex to the midpoint of the opposite side d) Nothing special about distances Warm-Up1Exercises EXAMPLE Relate side length and angle measure Draw an obtuse scalene triangle. Find the largest angle and longest side and mark them in red. Find the smallest angle and shortest side and mark them in blue. What do you notice? Warm-Up Exercises Notes Theorems 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. 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 shorter angle. Warm-Up Exercises GUIDED PRACTICE 1. List the sides of longest. for Examples 1 and 2 RST in order from shortest to Warm-Up Exercises Notes Theorem 5.10 Proof Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 2. There is a right triangle with sides that are 6, 8, o and 10 feet long and angles of 90 , about 37 , and o o about 53 . Sketch and label a diagram with the shortest side on the bottom and the right angle at the left. Warm-Up Exercises Notes Theorems Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Warm-Up3Exercises EXAMPLE Find possible side lengths ALGEBRA A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side. Warm-Up Exercises GUIDED PRACTICE for Example 3 3. A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side. Warm-Up Exercises Daily Homework Quick CheckQuiz In Exercises 1 and 2, list the sides or angles in order from least to greatest. 1. Tell whether the side lengths can form a triangle. 2. 37 m, 35 m, 18 m 3. 3 ft, 3 ft, 6 ft Warm-Up Exercises Daily Homework Quick CheckQuiz 4. Jeremy wants to build a triangular toy using sticks. He has one stick that is 12 inches and another that is 10 inches. What are the possible lengths of the third side of the triangle? Warm-Up Exercises For Tomorrow Homework HW: 5.5 (pg. 324-325) #10,14,16,24,35,39,44