1. Lesson 4 Menu 1.Write the assumption you would make to start an indirect proof of the statement: ΔABC is congruent to ΔDEF. 2.Write the assumption you would make to start an indirect proof of the statement: RS is an angle bisector. 3.Write the assumption you would make to start an indirect proof of the statement:  X is a right angle. 4.Write the assumption you would make to start an indirect proof of the statement: If 4x – 3  9, then x  3. 5.Write the assumption you would make to start an indirect proof of the statement: ΔMNO is an equilateral triangle.

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

3. Lesson 4 TH1

4. Lesson 4 Ex1 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.

5. Lesson 4 Ex1 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. 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. Check each inequality.

6. 1.A 2.B 3.C Lesson 4 CYP1 A. Determine whether 6, 9, 16 can be lengths of the sides of a triangle. A.yes B.no C.cannot be determined

7. 1.A 2.B 3.C Lesson 4 CYP1 B. Determine whether 14, 16, 27 can be lengths of the sides of a triangle. A.yes B.no C.cannot be determined

8. Lesson 4 Ex2 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

9. Lesson 4 Ex2 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. Determine Possible Side Lengths

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

11. Lesson 4 Ex2 Answer: D Examine the answer choices. The only value that does not satisfy the compound inequality is 13 since 13 is greater than 12.4. Thus, the answer is choice D. Determine Possible Side Lengths

12. Lesson 4 CYP2 1.A 2.B 3.C 4.D A.4 B.9 C.12 D.16 In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ?

13. Lesson 4 TH2

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

15. Lesson 4 Ex3 Prove Theorem 5.12 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 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. Proof: StatementsReasons 6. 6. Substitution 5. 5. Exterior Angle Inequality Theorem

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

17. Lesson 4 CYP3 Proof: Statements 1. 2. 3. 4. 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.

18. Lesson 4 CYP3 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.

19. 1.A 2.B 3.C 4.D Lesson 4 CYP3 A.Definition of inequality B.Substitution C.Triangle Inequality Theorem D.Exterior Angle Inequality Theorem

20. Lesson 4 CR1