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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?
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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
Write a two-column proof. Given: Prove: Use SAS Inequality in a Proof Lesson 5 Ex1
Proof: Statements Reasons 1. 1. Given 2. 2. Alternate interior angles are congruent. 3. Substitution 3. 4. 4. Subtraction Property 5. 5. Given 6. 6. Reflexive Property 7. 7. SAS Inequality Use SAS Inequality in a Proof Lesson 5 Ex1
Which reason correctly completes the two-column proof? Given:m1 < m3E is the midpoint of Prove:AC < AB Lesson 5 CYP1
Proof: Statements 1. 2.3.4.5.6.7.8. Reasons 1.Given2.Definition of midpoint3.Reflexive Property4.Given5. Vertical Angle Theorem6.Definition of congruent angles7.Substitution8._______________ E is the midpointof 2 3 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
Given: Prove: Prove Triangle Relationships Lesson 5 Ex2
Proof: Statements Reasons 1. 1. Given 2. 2. Reflexive Property 3. 3. Given 4. 4. Given 5. 5. Substitution 6. 6. SSS Inequality Prove Triangle Relationships Lesson 5 Ex2
Which reason correctly completes the following proof? Given:X is the midpoint ofΔMCX is isosceles.CB > CM Prove: Lesson 5 CYP2
Proof: Statements 1.2.3.4.5.6.7. Reasons 1.Given2.Definition of midpoint3.Given4.Definition of isosceles triangle5.Given6. Substitution7.______________ 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 mLDM to mMDN using the information in the figure. Lesson 5 Ex3
In ΔMDL and ΔMDN, The SSS Inequality allows us to conclude that Relationships Between Two Triangles Answer:mLDM > mMDN Lesson 5 Ex3
By the SSS Inequality, Relationships Between Two Triangles B. Write an inequality finding the range of values containing a using the information in the figure. 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
The two inequalities can be written as the compound inequality Relationships Between Two Triangles Lesson 5 Ex3
A. Compare mWYX and mZYW and write an inequality statement. • A • B • C • D A.mWYX < mZYW B.mWYX = mZYW C.mWYX > mZYW D.cannot be determined Lesson 5 CYP3
A.6 < n < 12 B. C.n > 6 D.6 < n < 18.3 B. Find the range of values containing n and write an inequality statement. • 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