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PROGRESS REPORTS TERM 2 – DEC 12TH 1. 2. 3. 4. TRIANGLE INEQUALITIES OBJECTIVE: TO USE INEQUALITIES INVOLVING THE SIDES AND ANGLES OF TRIANGLES 5. AGENDA Warm Up Quiz Return Notes Whiteboard Practice Exit Ticket THEOREM In a triangle, the longest side is across from the largest angle. In a triangle, the shortest side is across from the smallest angle. PRACTICE Example #1: Order the angles from smallest to largest. Example #2 Order the angles from smallest to largest THEOREM The sum of the lengths of any two sides of a triangle must be greater than the third side. b a c a+b> c b+c > a a+c > b If these inequalities are NOT true, you do not have a triangle! FINDING “POSSIBLE” LENGTHS Suppose we know the lengths of two sides of a triangle, and we want to find the “possible” lengths of the third side. IS IT A TRIANGLE? *REMEMBER*: THE SUM OF ANY 2 SIDES OF A TRIANGLE IS GREATER THAN THE THIRD SIDE. Decide whether each set of numbers is a triangle. 3. {3,4,5} 4. {3,5,10} 5. {5,5,10} EXAMPLE #6 The measures of two sides are given. Between what two numbers must the third side fall? Write an inequality to represent your answer. 9 and 15