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# Chapter 5-MATH ITU GUYS

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### Chapter 5-MATH ITU GUYS

1. 1. Inequalities in Triangles
2. 2. 1.4 in., 5 in., and the 8 in 2.2 in, 3 in and 5in 3.3 in, 4 in, and 8 in 4.2 in, 4 in, and 5 in 5.4 in, 5 in and 7 in
3. 3. FToHEr LtLh Threeoere ml i(nThee Lseegments to be the sides of a triangle, there must be a specific relationship among their lengths.
4. 4. Triangle Inequality Theorem In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
5. 5. Could it be less than? No, because if the third side was less than the sum of the other two sides, it would be shorter. Therefore, it would not be long enough to connect with the other two sides.
6. 6. Could it be equal to? No, because if the third side was equal to the sum of the other two sides, it would be the same length. Therefore, it would not make a triangle.
7. 7. Can you make a triangle in a 4in., 5in., and 12in.? No. 5+4 > 9 a + b > c b + c > a c + a > b
8. 8. 3 m, 4 m, and 1 m 5 yd, 13 yd, and 10 yd 24 in, 13, in, and 5 in
9. 9. Finding the Range of the Third Side Since the third side cannot be larger than the other two added together, we find the maximum value by adding the two sides. Since the third side and the smallest side given cannot be larger than the other side, we find the minimum value by subtracting the two sides. Difference < Third Side < Sum
10. 10. Example: a triangle has side lengths of 6 and 12; what are the possible lengths of the third side? B A C 6 12 X = ? 12 + 6 = 18 12 – 6 = 6 Therefore: 6 < X < 18
11. 11. Can the following lengths be the sides of a triangle? 1. 3, 4, 9 2. 2, 8, 6 3. 5, 12, 10 Find the range for the 3rd side of the following triangles when given the length of two sides. 4. 5, 12 5. 16, 22 6. 10, 3
12. 12. The Triangle Inequality Theorem 1. When you add the 2 smallest sides of a triangle, the answer is always ___________ than the third side. For 2-4, two sides of a triangle are given which can be the measure of the 3rd side? 2. 10, 18 a. 8 c. 20 b. 28 d. 5 3. 20, 5 a. 23 c. 30 b. 10 d. 15 4. 2, 8 a. 10 c. 6 b. 7 d. 15