1. Date: 7.5 Notes: The Δ Inequality Lesson Objective: Use the Δ Inequality Theorem to identify possible Δs and prove Δ relationships. CCSS: G.C0.10, G.MG.3

2. Lesson 1: The Δ Inequality Theorem Try to make triangles with the 2”, 3”, 5” and 6” straws given. List the straw sizes that can make triangles. List the straw sizes that cannot make triangles. What do you observe? Can Make Triangle:Cannot:

3. Lesson 1: The Δ Inequality Theorem Triangle Inequality Theorem: The sum of any 2 sides > the third side.

4. Lesson 2: Identifying Possible Δs Given Side Lengths To show that it is not possible to form a Δ with 3 side lengths, you need only show that 1 of the 3 Δ inequalities is not true.

5. Lesson 2: Identifying Possible Δs Given Side Lengths Tell whether a triangle can have sides with the given lengths. Explain. A.3, 5, 7 B.B.11, 6.5, 4 C.n + 5, n 2, 2n, when n = 3

6. Lesson 3: Finding the Side Lengths The lengths of 2 sides of a triangle are 5 cm and 11 cm. Find the range of possible lengths for the third side. 5 11 5 11

7. Lesson 4: Real-World Example The map shows the approximate distances from San Antonio to Austin, TX. What is the range of distances from Mason to Austin?

8. 7.5: Do I Get It? Tell whether a triangle can have sides with the given lengths. Explain. 1.8”, 15”, 17” 2.6 m, 8 m, 14 m 3. If the measures of 2 sides of a triangle are 3’ and 7’, what is the range of values for the third side?