1. Class Greeting

2. Objective: The students will apply Inequalities in One Triangle.

3. Exterior Angle Inequality Theorem
If an  is an exterior  of a ∆, then its measure is greater than the measure of either of its remote interior s.
m 1 > m 3 m 1 > m 4
m 5 > m 3 m 5 > m 2

4. Example 1
Use the Exterior Angle Inequality Theorem to list all of the angles whose measures are less than m14.
By the Exterior Angle Inequality Theorem,
m14 > m2,
m14 > m4,
m14 > m11,
and m14 > m4 + m3, therefore m14 > m3.
Answer: The angles that are greater than m14 are 2, 4, 11 and 3.

5. Example 2:
Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than m5.
By the Exterior Angle Inequality Theorem,
m10 > m5,
m12 > m5,
and m17 > m5.
Answer: The angles that are greater than m5 are
10, 12 and 17.

6. Your Turn:
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
a. all angles whose measures are less than m4
b. all angles whose measures are greater than m8
Answer: 5, 2, 8, 7
Answer: 4, 9, 5

7. The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

8. Example 2A: Ordering Triangle Side Lengths and Angle Measures
Write the angles in order from smallest to largest.
The shortest side is , so the smallest angle is F.
The longest side is , so the largest angle is G.
The angles from smallest to largest are F, H and G.

9. Example 2B: Ordering Triangle Side Lengths and Angle Measures
Write the sides in order from shortest to longest.
mR = 180° – (60° + 72°) = 48°
The smallest angle is R, so the shortest side is .
The largest angle is Q, so the longest side is .
The sides from shortest to longest are

10. Check It Out! Example 2a
Write the angles in order from smallest to largest.
The shortest side is , so the smallest angle is B.
The longest side is , so the largest angle is C.
The angles from smallest to largest are B, A, and C.

11. Check It Out! Example 2b
Write the sides in order from shortest to longest.
mE = 180° – (90° + 22°) = 68°
The smallest angle is D, so the shortest side is .
The largest angle is F, so the longest side is .
The sides from shortest to longest are

12. Kahoot!

13. Lesson Summary:
Objective: The students will apply Inequalities in One Triangle.

14. Preview of the Next Lesson:
Objective: The students will review for Lesson 5-1 to 5-3 test.

15. Stand Up Please