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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

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Apply the Triangle Inequality Theorem. Determine the shortest distance between a point and a line. http://www.geogebra.org/en/upload/files/english/dtravis/triangle_inequality.html http://www.geogebratube.org/student/m130 http://www.geogebra.org/en/upload/files/english/nebsary/TriangleInequality/TriangleInequalityFinal.html Lesson 4 MI/Vocab

Lesson 4 TH1

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

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

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

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

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

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 12.4. Thus, the answer is choice D. Answer: D Lesson 4 Ex2

Lesson 4 TH2

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

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

Lesson 4 CR1

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

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

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

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

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

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

End of Lesson 4