1. Splash Screen

2. Concept

3. Concept

4. By the Exterior Angle Theorem, you know that mÐ1 = mÐ2 + mÐ3.
The definition of inequality and the properties of inequalities can be applied to the measures of angles and segments, since these are real numbers. Consider Ð1, Ð2, and Ð3 in the figure shown.
By the Exterior Angle Theorem, you know that mÐ1 = mÐ2 + mÐ3.
Since the angle measures are positive numbers, we can also say that
mÐ1 > mÐ2 and mÐ1 > mÐ3
by the definition of inequality.
Concept

5. Concept

6. Use the Exterior Angle Inequality Theorem
Example 1

7. Use the Exterior Angle Inequality Theorem
Example 1

8. The longest side and largest angle of ∆ABC are opposite each other
The longest side and largest angle of ∆ABC are opposite each other. Likewise, the shortest side and smallest angle are opposite each other.
Concept

9. Concept

10. List the angles of ΔABC in order from smallest to largest.
Order Triangle Angle Measures
List the angles of ΔABC in order from smallest to largest.
Example 2

11. List the sides of ΔABC in order from shortest to longest.
Order Triangle Side Lengths
List the sides of ΔABC in order from shortest to longest.
Example 3

12. Angle-Side Relationships
HAIR ACCESSORIES Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie?
Example 4

13. End of the Lesson

14. Five-Minute Check (over Lesson 5–2) CCSS Then/Now
Key Concept: Definition of Inequality
Key Concept: Properties of Inequality for Real Numbers
Theorem 5.8: Exterior Angle Inequality
Example 1: Use the Exterior Angle Inequality Theorem
Theorems: Angle-Side Relationships in Triangles
Example 2: Order Triangle Angle Measures
Example 3: Order Triangle Side Lengths
Example 4: Real-World Example: Angle-Side Relationships
Lesson Menu

15. Find the coordinates of the centroid of the triangle with vertices D(–2, 9), E(3, 6), and F(–7, 0).
B. (–3, 4)
C. (–2, 5)
D. (–1, 4)
5-Minute Check 1

16. Find the coordinates of the orthocenter of the triangle with vertices F(–1, 5), G(4, 4), and H(1, 1). A. B.
C. (2, 3) D.
5-Minute Check 2

17. In ΔRST, RU is an altitude and SV is a median
In ΔRST, RU is an altitude and SV is a median. Find y if mRUS = 7y + 27.
___
A. 5
B. 7
C. 9
D. 11
5-Minute Check 3

18. In ΔRST, RU is an altitude and SV is a median.
___
Find RV if RV = 6a + 3 and RT = 10a + 14.
A. 3
B. 4
C. 21
D. 27
5-Minute Check 4

19. Which of the following points is the center of gravity of a triangle?
A. centroid
B. circumcenter
C. incenter
D. orthocenter
5-Minute Check 5

20. G.CO.10 Prove theorems about triangles. Mathematical Practices
Content Standards
G.CO.10 Prove theorems about triangles.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
CCSS

21. You found the relationship between the angle measures of a triangle.
Recognize and apply properties of inequalities to the measures of the angles of a triangle.
Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.
Then/Now