5.6 inequalities 1 triangle.notebook
11/8/16 - Warm Up Problem
Fill in the blank with a < or > sign.
November 08, 2016
5.6 inequalities 1 triangle.notebook
November 08, 2016
5.6 inequalities 1 triangle.notebook
November 08, 2016
5.6 inequalities 1 triangle.notebook
November 08, 2016
Section 5.5 ‐ Inequalities in Triangles
Goals: Use the Triangle Inequality to determine the lengths of
sides that will make a triangle, and find a range of possible
lengths for the third side when given two sides of a triangle.
List the angles in order
from smallest to largest.
List the sides in order from
shortest to longest.
J
A
53o
13
9
41o
86o
C
18
B
L
K
5.6 inequalities 1 triangle.notebook
November 08, 2016
Spaghetti Geometry
Can you make a triangle out of any three pieces or do they have to be certain lengths?
1. Cut five pieces of spaghetti to be 3 inches, 4 inches, 5 inches, 7 inches, and 8 in.
2. Use the 3 in, 4 in, and 5 in. pieces.
• do they make a triangle?
3. Use the 3 in, 4 in, and 7 in. pieces.
• do they make a triangle?
4. Use the 3 in, 4 in, and 8 in. pieces.
• do they make a triangle?
5.6 inequalities 1 triangle.notebook
November 08, 2016
The Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
2
4
5
To simplify: The sum of the shortest two sides must be greater than the longest side
5.6 inequalities 1 triangle.notebook
Using the Triangle Inequality Theorem
November 08, 2016
5.6 inequalities 1 triangle.notebook
November 08, 2016
Finding Possible Side Lengths
A triangle has sides of lengths 8 cm and 10 cm.
Describe the lengths possible for the third side.
Step 1: Assume the missing side is the longest side
Step 2: Assume the missing side is one of the shorter sides
Step 3: Put it together as a compound inequality
5.6 inequalities 1 triangle.notebook
Finding Possible Side Lengths
A triangle has sides of lengths 3 in. and 12 in.
Describe the lengths possible for the third side.
A triangle has sides of lengths 1.5 cm and 5.5 cm.
Describe the lengths possible for the third side.
November 08, 2016
5.6 inequalities 1 triangle.notebook
Assignment:
pg. 329
(21­32)
(37­39)
November 08, 2016