1. BASIC GEOMETRY Section 5: Inequalities in one Triangle

2. Angle-Side Relationships in a Triangle
In a triangle, the larger ∠ is opposite the longer side.
In a triangle, the longer side is opposite the larger ∠.

3. Example 1

4. Triangle Inequality Theorem:
The sum of any two sides of a triangle must be greater than the third side
What?

5. How to tell if 3 lengths can make a triangle?
Shortcut: Add the two smallest sides & check to see if it is bigger than the third side.
7, 10, 19
2.3, 3.1, 4.6
3, 5, 8
n + 6, n2 – 1, 3n, when n = 4

6. Find a range of possible lengths for third side if you’re given 2 sides.
7cm A
7cm B B
5 cm
5 cm
5 cm
7cm A
5 cm
7cm
5 cm
5 cm
7cm
7cm B B A A
For this to form a triangle, 2 cm < AB < 12 cm

7. Example ?
The lengths of two sides of a triangle are 8in & 13in. Find the range of possible lengths for the third side.

8. Example ??
The figure shows the approximate distances between cities in California. What is the range of distances from San Francisco to Oakland?

9. Assignment #5 page 336 #’s 4-15,(78)