1. Lesson 5-5: Inequalities in Triangles

2. Angle-Side Relationship
Think of two flashlights shining on a wall
• The flashlight with the widest opening makes a longer segment
on the opposite wall, similarly…
► The widest angle has the longest side opposite to it.
► The narrowest angle has the shortest side opposite to it.

3. Write the measurements of the triangles in order from least to greatest.
100˚ H J G
45˚
35˚ 8 5 Q R P 7
SOLUTION
SOLUTION JH
< JG
< GH
m R
< mQ
< m P

4. Can you make a triangle with any 3 sides?
Draw a triangle with sides 3, 6, and 8 inches
Draw a triangle with sides 3, 6, and 9 inches
Draw a triangle with sides 3, 6, and 10 inches.

5. 3 Sides Inequality Any 2 sides must be greater than the 3rd side
Testing 3 sides
2 smaller sides must be more than 3rd side
Range for 3rd side
Order sides
Subtract left, add right
3rd side must be between (not equal! )

6. Can 13, 21, 33 be the sides of a triangle?
Given 12 cm and 15 cm, what are the possibilities for the 3rd side?
Two smaller sides: = ?
= 34 → bigger than 3rd side → YES
Order, subtract left, add right
15 – 12 = 3; = 27
3rd side must be between 3 and 27 → 3 < 3rd side < 27