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TOPIC 5-2: TRIANGLE INEQUALITIES Use the straws and string to find out if a triangle can be made. Sides Could a Classify by Sum of >, <, or Larger triangle be Sides shorter = side made: sides Yes or No? 2 2 2 2 2 3 2 3 4 2 3 5 2 3 6 3 4 5 3 3 6 3 3 3 3 3 4 3 5 6 What did you find out ? In order for a triangle to be constructed, the sum of the smaller sides must be ______________________the larger side. EXAMPLES: Determine if the following sides will make a triangle and if yes, then classify by sides. 1. 8, 9, 10 yes or no ______________________ 2. 1, 1, 2 yes or no ______________________ 3. 6, 6, 10 yes or no ______________________ 4. 3, 5, 7 yes or no ______________________ 5. 4, 4, 4 yes or no ______________________ EXAMPLE 6: If two sides of a triangle are 3 and 7, what range of numbers would be possible for the length of the third side? EXAMPLE 7: If two sides of a triangle are 9 and 20, what range of numbers would be possible for the length of the third side? In a triangle the largest side is opposite the largest angle, and the smallest side is opposite the smallest angle. EXAMPLE 8: A = 120, B = 40, C = 20 B Largest side: C A Smallest side: EXAMPLE 9 Classify the triangle by sides, then list the angles from small to large. B 12 70 A 70 15 9 C Classify:_________________ Angles:______, ______, ______ EXAMPLE 10 List the sides of ABC in order from longest to shortest if the angles of ABC have the indicated measures: mA = (10x), mB = (5x – 17), mC = (7x –1).