1. 5.5 Inequalities in Triangles
DOM
Can you figure out the puzzle below???
Domino

2. Comparison Property of Inequalityb c
Comparison Property of Inequality:
If a = b + c, and c > 0, then a > b.

3. Proof of Comparison Property of Inequality
Given: a = b + c, c > 0
Prove: a > b
Statements
Reasons 1. 2. 3. 4. 5.
c > 0
b + c > b + 0
b + c > b
a = b + c
a > b

4. Theorem
Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
Insert figure from home

5. Application Given the figure below, explain why . 1. 1. 2. 2. 3. 3.
Statements
Reasons 1. 2. 3. 1. 2. 3. 5

6. Theorem
Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
Insert figure from home 6

7. Example
List the angles of the following figure in order from smallest to largest. 7

8. Theorem
Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
Insert figure from home 8

9. Sides of a Triangle
List the sides of the following triangle in order from shortest to longest.
Determine which segment is shortest in the following diagram.

10. Theorem
Theorem 5-12: Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Insert figure from home 10

11. Theorem Can a triangle have sides with the given lengths?
a) 7 ft, 3 ft, 8 ft
b) 10 cm, 6 cm, 3 cm
A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side. 11

12. 5.5 Inequalities in Triangles
HW 5.5: #1-25 (1st column), 32, 33, 35
p.192: #3-4, 11, 22, 24-26
Scrambled Eggs

13. Midterm Review
Given the figure below, name the type of angle pairs given.

14. Midterm Review
Find Justify each answer. 1) 2)
135° 1 2 14

15. Midterm Review
Find x in the following polygon. x°
125°
125° 15

16. Midterm Review
Find the equation of a line that goes through the point (-2, 1) and (3,2).
Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5). 16