Recognize and apply properties of inequalities to the measures of angles of a triangle. Recognize and apply properties of inequalities to the relationships.

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Presentation transcript:

Recognize and apply properties of inequalities to the measures of angles of a triangle. Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle. Lesson 2 MI/Vocab

Lesson 2 KC1

Compare Angle Measures Determine which angle has the greatest measure. Plan Use properties and theorems of real numbers to compare the angle measures. Lesson 2 Ex1

Determine which angle has the greatest measure. B.  3 C.  5 D.  4 A B C D Lesson 2 CYP1

Lesson 2 TH1

Exterior Angles Lesson 2 Ex2

Exterior Angles Since 11 and 9 are vertical angles, they have equal measure, so m14 > m9. m9 > m6 and m9 > m7, so m14 > m6 and m14 > m7. Lesson 2 Ex2

Exterior Angles Lesson 2 Ex2

Exterior Angles Lesson 2 Ex2

Lesson 2 TH2

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

Side-Angle Relationships C. Determine the relationship between the measures of RSV and RUV. Theorem 5.9 Theorem 5.9 Addition Property of Inequality Angle Addition Lesson 2 Ex3

Side-Angle Relationships 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

Lesson 2 TH3

Angle-Side Relationships HAIR ACCESSORIES Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie? Lesson 2 Ex4

Angle-Side Relationships Theorem 5.10 states that 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. Since X is opposite the longest side it has the greatest measure. Answer: So, Ebony should tie the ends marked Y and Z. Lesson 2 Ex4