1. Kiley plans to fly over the route marked on the map of Hawaii.
If m∠A = x + 2, m∠B = x, and m∠C = 2x – 14, what are the measures of the three angles?
What are the lengths of Kiley’s trip in order of least to greatest?
Problem of the Day

2. Section 5-5 The Triangle Inequality

3. Then
Now
Objectives
You recognized and applied properties of inequalities to the relationships between the angles and sides of a triangle.
Use the Triangle Inequality Theorem to identify possible triangles.

4. Common Core State Standards
Content Standards
G.CO.10 – Prove theorems about triangles.
G. MG.3 – Apply geometric methods to solve problems.
Mathematical Practices
1) Make sense of problems and persevere in solving them.
2) Reason abstractly and quantitatively.
Common Core State Standards

5. Triangle Inequality Theorem

6. Is it possible to form a triangle with the given side lengths
Is it possible to form a triangle with the given side lengths? If not, explain why.
15 yd, 16 yd, 30 yd
2 ft, 8 ft, 11 ft
Example 1

7. Is it possible to form a triangle with the given side lengths
Is it possible to form a triangle with the given side lengths? If not, explain why.
6.5, 6.5, 13.5
5.1, 6.8, 7.2
Example 1

8. Is it possible to form a triangle with the given side lengths
Is it possible to form a triangle with the given side lengths? If not, explain why.
1 3 4 , , 5 1 8
1 1 5 , , 4 1 2
Example 1

9. Triangle Inequality Theorem Continued
When given the lengths of two sides of a triangle, you can use the Triangle Inequality Theorem to find the range of values that the third side could be.
Triangle Inequality Theorem Continued
If the lengths two sides of a triangle are 2 and 3, what is the range for the length of the third side?

10. Difference of Two Sides
Sum of Two Sides
<
Third Side
<

11. Example 2 Which of the following could NOT be the value of n? 7 10 1322
Example 2

12. Example 2 In ∆PQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR?9 11 13
Example 2

13. Find the range for the length of the third side of a triangle given the lengths of two sides.
6 ft and 19 ft
7 km and 29 km
6 m and 42 m
13 in. and 27 in.
Example 2

14. p.366 #1 – 4, 6 – 9, 24 – 26, 55
Homework