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Lesson 4.3 Angle Bisectors pp. 129-134

Lesson 4.3 Angle Bisectors pp. 129-134. Objectives: 1. To identify and apply the Angle Addition Postulate. 2. To define and apply angle bisectors. 3. To define and identify perpendicular lines. Definition.

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Lesson 4.3 Angle Bisectors pp. 129-134

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  1. Lesson 4.3 Angle Bisectors pp. 129-134

  2. Objectives: 1. To identify and apply the Angle Addition Postulate. 2. To define and apply angle bisectors. 3. To define and identify perpendicular lines.

  3. Definition Adjacent angles are two coplanar angles that have a common side and common vertex but no common interior points.

  4. B D A C DAB and DAC are called adjacent angles.

  5. B D A C BAC and DAC are NOT adjacent angles.

  6. B C A E D BAC and CDE are NOT adjacent angles.

  7. Postulate 4.3 Angle Addition Postulate. If K lies in the interior of MNP, then mMNP = mMNK + mKNP.

  8. X T Z Y Example 1 Find mXYZ if mXYT = 25° and mTYZ = 15°. mXYZ =mXYT + mTYZ mXYZ = 25 + 15 mXYZ = 40°

  9. C D A B Example 2 Find mDBC if mABC = 90° and mABD = 70°. mABC =mABD + mDBC 90 = 70 + mDBC 20° = mDBC

  10. B D A C Find mBAC if mBAD = 35 and mDAC = 15.

  11. Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the interior of ARV, find mQRV.

  12. Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the interior of ARV, find mQRV. A 30° 70° R 40° Q V

  13. Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the exterior of ARV, find mQRV.

  14. Given mARQ = 30°, mARV = 70°, and mQRJ = 5°. If Q is in the exterior of ARV, find mQRV. V A 100° 70° Q 30° R

  15. Definition Anangle bisector is a ray that (except for its origin) is in the interior of an angle and forms congruent adjacent angles.

  16. Definition Perpendicular lines are lines that intersect to form right angles. The symbol for perpendicular is .

  17. Homework pp. 133-134

  18. V W U Z Y X ►A. Exercises 11. Find mUYX if mUYW = 75° and mWYX = 35°.

  19. V W U Z Y X ►B. Exercises 13. Find mUYV if mUYW = 85° and mVYW = 15°.

  20. ►B. Exercises 15. If FD is the bisector of EFC, what is true about 1 and 5? E D 1 C 5 F 2 4 3 A B

  21. ►B. Exercises 17. If FC bisects DFB and mDFB = 92°, what is m5? E D 1 C 5 F 2 4 3 A B

  22. ■ Cumulative Review In each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem. 26. plane, space

  23. ■ Cumulative Review In each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem. 27. point, line

  24. ■ Cumulative Review In each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem. 28. polygon, plane

  25. ■ Cumulative Review In each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem. 29. line, plane

  26. ■ Cumulative Review In each problem, identify the sets into which the first figure divides the second. Justify your answer with a postulate or theorem. 30. polyhedron, space

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