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Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Lesson 5-1 Bisectors, Medians, and Altitudes Lesson 5-2 Inequalities and Triangles Lesson 5-3 Indirect Proof Lesson 5-4 The Triangle Inequality Lesson 5-5 Inequalities Involving Two Triangles Example 1 Compare Angle Measures Example 2 Exterior Angles Example 3 Side-Angle Relationships Example 4 Angle-Side Relationships Determine which angle has the greatest measure. Explore Compare the measure of 1 to the measures of 2, 3, 4, and 5. Plan Use properties and theorems of real numbers to compare the angle measures. Solve Compare m3 to m1. By the Exterior Angle Theorem, m1 m3 m4. Since angle measures are positive numbers and from the definition of inequality, m1 > m3. Compare m4 to m1. By the Exterior Angle Theorem, m1 m3 m4. By the definition of inequality, m1 > m4. Compare m5 to m1. Since all right angles are congruent, 4 5. By the definition of congruent angles, m4 m5. By substitution, m1 > m5. Compare m2 to m5. By the Exterior Angle Theorem, m5 m2 m3. By the definition of inequality, m5 > m2. Since we know that m1 > m5, by the Transitive Property, m1 > m2. Examine The results on the previous slides show that m1 > m2, m1 > m3, m1 > m4, and m1 > m5. Therefore, 1 has the greatest measure. Answer: 1 has the greatest measure. Determine which angle has the greatest measure. Answer: 5 has the greatest measure. Use the Exterior Angle Inequality Theorem to list all angles whose measures are less than m14. By the Exterior Angle Inequality Theorem, m14 > m4, m14 > m11, m14 > m2, and m14 > m4 + m3. Since 11 and 9 are vertical angles, they have equal measure, so m14 > m9. m9 > m6 and m9 > m7, so m14 > m6 and m14 > m7. Answer: Thus, the measures of 4, 11, 9, 3, 2, 6, and 7 are all less than m14 . Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than m5. By the Exterior Angle Inequality Theorem, m10 > m5, and m16 > m10, so m16 > m5, m17 > m5 + m6, m15 > m12, and m12 > m5, so m15 > m5. Answer: Thus, the measures of 10, 16, 12, 15 and 17 are all greater than m5. Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. a. all angles whose measures are less than m4 Answer: 5, 2, 8, 7 b. all angles whose measures are greater than m8 Answer: 4, 9, 5 End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.