1. Concept

2. Example 1 Identify Possible Triangles Given Side Lengths A. Is it possible to form a triangle with side lengths of 6, 6, and 14 ? If not, explain why not. __ 1 2 1 2 1 2 Check each inequality. Answer: X

3. Example 1 Identify Possible Triangles Given Side Lengths B. Is it possible to form a triangle with side lengths of 6.8, 7.2, 5.1? If not, explain why not. Answer: yes Check each inequality. 6.8 + 7.2> 5.17.2 + 5.1 > 6.86.8 + 5.1> 7.2 14> 5.1  12.3> 6.8  11.9> 7.2  Since the sum of all pairs of side lengths are greater than the third side length, sides with lengths 6.8, 7.2, and 5.1 will form a triangle.

4. Example 1 A.yes B.no

5. Example 1 A.yes B.no B. Is it possible to form a triangle given the side lengths 4.8, 12.2, and 15.1?

6. Example 2 In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR? A 7 B 9 C 11 D 13 Find Possible Side Lengths

7. Example 2 Read the Test Item You need to determine which value is not valid. Solve the Test Item Solve each inequality to determine the range of values for PR. or n < 12.4 Find Possible Side Lengths

8. Example 2 Notice that n > –2 is always true for any whole number measure for x. Combining the two remaining inequalities, the range of values that fit both inequalities is n > 2 and n < 12.4, which can be written as 2 < n < 12.4. Find Possible Side Lengths

9. Example 2 Answer: D Examine the answer choices. The only value that does not satisfy the compound inequality is 13 since 13 is greater than 12.4. Thus, the answer is choice D. Find Possible Side Lengths

10. Example 2 A.4 B.9 C.12 D.16 In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ?

11. Example 3 Proof Using Triangle Inequality Theorem TRAVEL The towns of Jefferson, Kingston, and Newbury are shown in the map below. Prove that driving first from Jefferson to Kingston and then Kingston to Newbury is a greater distance than driving from Jefferson to Newbury.

12. Example 3 Proof Using Triangle Inequality Theorem Answer: By the Triangle Inequality Theorem, JK + KN > JN. Therefore, driving from Jefferson to Kingston and then Kingston to Newbury is a greater distance than driving from Jefferson to Newbury. Abbreviating the vertices as J, K, and N: JK represents the distance from Jefferson to Kingstown; KN represents the distance from Kingston to Newbury; and JN the distance from Jefferson to Newbury.

13. Example 3 A.Jacinda is correct, HC + CG > HG. B.Jacinda is not correct, HC + CG < HG. Jacinda is trying to run errands around town. She thinks it is a longer trip to drive to the cleaners and then to the grocery store, than to the grocery store alone. Determine whether Jacinda is right or wrong.