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Lesson 7.3 Exterior Angles and Inequalities pp. 273-278

Lesson 7.3 Exterior Angles and Inequalities pp. 273-278. Objectives: 1. To review the real number properties of inequality and apply them to exterior angles. 2. To prove and apply the relation between an exterior angle and the two remote interior angles. Definition.

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Lesson 7.3 Exterior Angles and Inequalities pp. 273-278

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  1. Lesson 7.3 Exterior Angles and Inequalities pp. 273-278

  2. Objectives: 1. To review the real number properties of inequality and apply them to exterior angles. 2. To prove and apply the relation between an exterior angle and the two remote interior angles.

  3. Definition An exterior angle of a triangle is an angle that forms a linear pair with one of the angles of the triangle.

  4. 1 2 3 4 5 6 9 7 8

  5. Definition The remote interior angles of an exterior angle are the two angles of the triangle that do not form a linear pair with a given exterior angle.

  6. D A B C ABD is an exterior angle of BCD. C and D are remote interior angles of ABD.

  7. 4 5 1 6 2 3 9 7 8

  8. Theorem 7.10 Exterior Angle Theorem. The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

  9. O 87° 42° N P M Find mMNP.

  10. Theorem 7.11 Exterior Angle Inequality. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

  11. D 110° 33° A B C Practice: Find mABD. 70°

  12. W 76° X Y Z Practice: Find mWZY. 52°

  13. W 76° X Y Z Practice: Find mWYX. 128°

  14. Homework pp. 275-278

  15. A 65º B C D ►A. Exercises Find the measure of the indicated angles. 1. mA

  16. A 65º B C D ►A. Exercises Find the measure of the indicated angles. 1. mBCA

  17. A 65º B C D ►A. Exercises Find the measure of the indicated angles. 1. mACD

  18. O N x x - 60º x - 20º L M ►A. Exercises Find the measure of the indicated angles. 5. mONL

  19. O N x x - 60º x - 20º L M ►A. Exercises Find the measure of the indicated angles. 5. mLNM

  20. O N x x - 60º x - 20º L M ►A. Exercises Find the measure of the indicated angles. 5. mL

  21. O N x x - 60º x - 20º L M ►A. Exercises Find the measure of the indicated angles. 5. mM

  22. C 80º x 60º A 40º B ►A. Exercises Refer to ABC; give the measure of the exterior angles at each vertex. 7. A

  23. 60º ►A. Exercises 11. If ABC is equilateral, what is the measure of an exterior angle?

  24. 78º ►B. Exercises 13. If an exterior angle at the vertex of an isosceles triangle measures 78 degrees, what are the measures of the base angles?

  25. D C A B ►B. Exercises 15. If ABCD is a rhombus and C-D-E, what is the relationship between mEDA and mDAC?

  26. E D C A B ►B. Exercises 15. If ABCD is a rhombus and C-D-E, what is the relationship between mEDA and mDAC?

  27. q r ■ Cumulative Review How does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case. 24.

  28. a b c ■ Cumulative Review How does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case. 25.

  29. s r t ■ Cumulative Review How does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case. 26.

  30. n l m ■ Cumulative Review How does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case. 27.

  31. p g h ■ Cumulative Review How does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case. 28.

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