Inequalities and Triangles pp. 280 – 287 & 296 - 301 DNA Chapters 5 – 2 & 5 - 4 Inequalities and Triangles pp. 280 – 287 & 296 - 301

(over Lesson 5-1) In the figure, A is the point of concurrency of the perpendicular bisectors of ΔLMN. Find x if mAPM = 7x + 13. A. 23.86 B. 21 C. 11 D. 8.86 5Min 2-2

(over Lesson 5-1) In ΔRST, RU is an altitude and SV is a median. Find y if mRUS = 7y + 27. A. 63 B. 27 C. 12 D. 9 5Min 2-4

(over Lesson 5-1) In ΔRST, RU is an altitude and SV is a median. Find RV if RV = 6a + 3 and RT = 10a + 14. A. 4 B. 24 C. 27 D. 63 5Min 2-5

Which congruence statement is true if P is the circumcenter of ΔWXY? (over Lesson 5-1) Which congruence statement is true if P is the circumcenter of ΔWXY? A. WX  XY B. WP  XP C. WP  WX D. WY  XY A B C D 5Min 2-6

Exterior Angle Inequality Theorem If an angle is an exterior of a , then its measure > the measure of either of its corresponding remote interior . A B C 1 2 3 4

Exterior Angles Lesson 2 Ex2

A B C D A. B. C. D. Lesson 2 CYP2

A. B. C. D. A B C D Lesson 2 CYP2

OppositeAngle measure B Side length 2 in. 1.7 in. C A 1 in.

B Theorem 5.9 If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. 2 in. 1.7 in. C A 1 in.

B Theorem 5.10 If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. 2 in. 1.7 in. C A 1 in.

Side-Angle Relationships A. Determine the relationship between the measures of RSU and SUR. Lesson 2 Ex3

Side-Angle Relationships B. Determine the relationship between the measures of TSV and STV. Lesson 2 Ex3

A B C D A. B. C. D. cannot be determined Lesson 2 CYP3

AED and EAD. A. mAED < mEAD B. mAED = mEAD C D A. mAED < mEAD B. mAED = mEAD C. mAED > mEAD D. cannot be determined Lesson 2 CYP3

EAB and EDB. A. mEAB < mEDB B. mEAB = mEDB C D A. mEAB < mEDB B. mEAB = mEDB C. mEAB > mEDB D. cannot be determined Lesson 2 CYP3

Triangle Inequality B 2 in. 1.7 in. C A 1 in.

Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the 3rd side.

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

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

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

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

Determine whether the given coordinates are the vertices of a triangle Determine whether the given coordinates are the vertices of a triangle. Explain. 1 (-2) -2 (-2) 3+4>5 4+5>3 5+3>4 Yes -2 (-2) 2 (-2) -2 1 2 (-2)

Homework: Textbook pp. 284 – 287, problems 1 – 9 and 28 – 32 even pp. 299 – 300, Problems 1 – 5, 8 – 18 even, and 23 – 26.

Textbook pp. 284 – 287, problems 1 – 9 and 28 – 32 even

pp. 299 – 300, 1 – 5, 8 – 18 even, and 23 – 26

ALGEBRA Determine whether the given coordinates of the vertices of a triangle. Explain.