Can the measure of 5, 7, and 8 be the lengths of the sides of a triangle? Can the measures 4.2, 4.2, and 8.4 be the lengths of the sides of a triangle?

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Can the measure of 5, 7, and 8 be the lengths of the sides of a triangle? Can the measures 4.2, 4.2, and 8.4 be the lengths of the sides of a triangle? Can the measures 3, 6, and 10 be the lengths of the sides of a triangle? Find the range for the measure of the third side of a triangle if two of its sides measure 4 and 13. Find the range for the measure of the third side of a triangle if two of its sides measure 8.3 and 15.6. Lesson 5 Menu

Apply the SAS Inequality. Apply the SSS Inequality. Lesson 5 MI/Vocab

Lesson 5 TH1

Use SAS Inequality in a Proof Write a two-column proof. Given: Prove: Lesson 5 Ex1

Use SAS Inequality in a Proof Statements Reasons 1. 1. Given 2. 2. Alternate interior angles are congruent. 3. 3. Substitution 4. 4. Subtraction Property 5. 5. Given 6. 6. Reflexive Property 7. 7. SAS Inequality Lesson 5 Ex1

Which reason correctly completes the two-column proof? Prove: AC < AB Given: m1 < m3 E is the midpoint of Lesson 5 CYP1

Proof: Statements 1. 2. 3. 4. 5. 6. 7. 8. Reasons 1. Given 2. Definition of midpoint 3. Reflexive Property 4. Given 5. Vertical Angle Theorem 6. Definition of congruent angles 7. Substitution 8. _______________ 2  3 E is the midpoint of Lesson 5 CYP1

A. SSS Inequality Theorem B. SAS Inequality Theorem C. Substitution D. none of the above A B C D Lesson 5 CYP1

Lesson 5 TH2

Prove Triangle Relationships Given: Prove: Lesson 5 Ex2

Prove Triangle Relationships Proof: Statements Reasons 1. 1. Given 2. 2. Reflexive Property 3. 3. Given 4. 4. Given 5. 5. Substitution 6. 6. SSS Inequality Lesson 5 Ex2

Which reason correctly completes the following proof? Given: X is the midpoint of ΔMCX is isosceles. CB > CM Prove: Lesson 5 CYP2

Proof: Statements 1. 2. 3. 4. 5. 6. 7. Reasons 1. 2. 3. 4. 5. 6. 7. Reasons 1. Given 2. Definition of midpoint 3. Given 4. Definition of isosceles triangle 5. Given 6. Substitution 7. ______________ X is the midpoint of ΔMCX is isosceles. Lesson 5 CYP2

A. SSS Inequality Theorem B. SAS Inequality Theorem C. Substitution D. none of the above A B C D Lesson 5 CYP2

Relationships Between Two Triangles A. Write an inequality relating mLDM to mMDN using the information in the figure. Lesson 5 Ex3

Relationships Between Two Triangles In ΔMDL and ΔMDN, The SSS Inequality allows us to conclude that Answer: mLDM > mMDN Lesson 5 Ex3

Relationships Between Two Triangles B. Write an inequality finding the range of values containing a using the information in the figure. By the SSS Inequality, Lesson 5 Ex3

Relationships Between Two Triangles SSS Inequality Substitution Subtract 15 from each side. Divide each side by 9. Also, recall that the measure of any angle is always greater than 0. Subtract 15 from each side. Divide each side by 9. Lesson 5 Ex3

Relationships Between Two Triangles The two inequalities can be written as the compound inequality Lesson 5 Ex3

A. Compare mWYX and mZYW and write an inequality statement. A. mWYX < mZYW B. mWYX = mZYW C. mWYX > mZYW D. cannot be determined A B C D Lesson 5 CYP3

B. Find the range of values containing n and write an inequality statement. C. n > 6 D. 6 < n < 18.3 A B C D Lesson 5 CYP3

Use Triangle Inequalities HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Nitan can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which foot can Nitan raise higher above the table? Assume both of Nitan’s legs have the same measurement, the SAS Inequality tells us that the height of the left foot opposite the 65° angle is higher than the height of his right foot opposite the 35° angle. This means that his left foot is raised higher. Answer: his left foot Lesson 5 Ex4

HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Megan can lift her right foot 18 inches from the table and her left foot 13 inches from the table. Which leg makes the greater angle with the table? A B C A. her right leg B. her left leg C. neither Lesson 5 CYP4