1. Concept

2. Example 1 Identify Possible Triangles Given Side Lengths A. Is it possible to form a triangle with the given 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 the given 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. A.A B.B Example 1 A.yes B.no

5. A.A B.B 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

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

8. 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.

9. 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 side of the triangle from Jefferson to Kingstown; KN represents the side of the triangle from Kingston to Newbury; and JN the side of the triangle from Jefferson to Newbury.

10. A.A B.B 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.

11. Find the range of possible measures of x if each set of expressions represents measures of the sides of a triangle: 1. x, 4, 6 2 < x < 10

12. 2.x – 2, 10, 12 4 < x < 24

13. 3.x + 2, x + 4, x + 6 x > 0