1. Splash Screen

2. Five-Minute Check (over Lesson 5-3) Main Ideas California Standards
Theorem 5.11: Triangle Inequality Theorem
Example 1: Identify Sides of a Triangle
Example 2: Standards Example: Determine Possible Side Length
Theorem 5.12
Example 3: Prove Theorem 5.12
Corollary 5.1
Lesson 4 Menu

3. Do Now

4. Do Now

5. Apply the Triangle Inequality Theorem.
Determine the shortest distance between a point and a line.
Lesson 4 MI/Vocab

6. Lesson 4 TH1

7. Identify Sides of a Triangle
Answer: Because the sum of two measures is not greater than the length of the third side, the sides cannot form a triangle.
Lesson 4 Ex1

8. Identify Sides of a Triangle
B. Determine whether the measures 6.8, 7.2, and 5.1 can be lengths of the sides of a triangle.
Check each inequality.   
Answer: All of the inequalities are true, so 6.8, 7.2, and 5.1 can be the lengths of the sides of a triangle.
Lesson 4 Ex1

9. Determine Possible Side Lengths
In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR?
A 7
B 9
C 11
D 13
Lesson 4 Ex2

10. Determine Possible Side Lengths
Read the Item
You need to determine which value is not valid.
Solve the Item
Solve each inequality to determine the range of values for PR.
Lesson 4 Ex2

11. Determine Possible Side Lengths
Graph the inequalities on the same number line.
The range of values that fit all three inequalities is
Lesson 4 Ex2

12. Determine Possible Side Lengths
Examine the answer choices. The only value that does not satisfy the compound inequality is 13 since 13 is greater than Thus, the answer is choice D.
Answer: D
Lesson 4 Ex2

13. Lesson 4 TH2

14. Given: Line through point J Point K lies on t.
Prove Theorem 5.12
Given: Line through point J Point K lies on t.
Prove: KJ < KH H K
Lesson 4 Ex3

15. 2. Perpendicular lines form right angles.
Prove Theorem 5.12
Proof:
Statements
Reasons 1.
1. Given
are right angles. 2.
2. Perpendicular lines form right angles. 3.
3. All right angles are congruent. 4.
4. Definition of congruent angles 5.
5. Exterior Angle Inequality Theorem 6.
6. Substitution 7.
7. If an angle of a triangle is greater than a second angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Lesson 4 Ex3

16. Lesson 4 CR1

18. A. Determine whether 6, 9, 16 can be lengths of the sides of a triangle.
A. yes
B. no
C. cannot be determined A B C
Lesson 4 CYP1

19. B. Determine whether 14, 16, 27 can be lengths of the sides of a triangle.
A. yes
B. no
C. cannot be determined A B C
Lesson 4 CYP1

20. In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ?
Lesson 4 CYP2

21. Choose the correct reason to complete the following proof.
Prove: AB > AD
Given: is an altitude in ΔABC.
Lesson 4 CYP3

22. Proof: Statements 1. 2. 3. 4. Reasons
Reasons
1. Given 2. Definition of altitude 3. Perpendicular lines form right angles. 4. All right angles are congruent.
is an altitude in ΔABC.
are right angles.
Lesson 4 CYP3

23. Proof: Statements 5. 6. 7. 8. Reasons
5. Definition of congruent angles 6. _____________ 7. Substitution 8. If an angle of a triangle is greater than a second angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Lesson 4 CYP3

24. A. Definition of inequality B. Substitution
C. Triangle Inequality Theorem
D. Exterior Angle Inequality Theorem A B C D
Lesson 4 CYP3

25. End of Lesson 4