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Lesson 4.4 Angle Properties pp. 135-141

Lesson 4.4 Angle Properties pp. 135-141. Objectives: 1. To identify linear pairs and vertical, complementary, and supplementary angles. 2. To prove theorems on related angles. D. A. B. C. Definition.

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Lesson 4.4 Angle Properties pp. 135-141

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  1. Lesson 4.4 Angle Properties pp. 135-141

  2. Objectives: 1. To identify linear pairs and vertical, complementary, and supplementary angles. 2. To prove theorems on related angles.

  3. D A B C Definition A linear pair is a pair of adjacent angles whose noncommon sides form a straight angle (are opposite rays).

  4. Definition Vertical angles are angles adjacent to the same angle and forming linear pairs with it. E A B C D

  5. Definition Two angles are complementary if the sum of their measures is 90°. Two angles are supplementary if the sum of their measures is 180°.

  6. C Y 67° 23° T F X CFY and YFX are complementary

  7. C Y 157° 23° T F X TFY and YFX are supplementary

  8. Theorem 4.1 All right angles are congruent.

  9. STATEMENTSREASONS A and B are Given right angles 12. mA = 90° 12. _______________ mB = 90° 13. mA = mB 13. _______________ 14. A  B 14. _______________ Def. of rt. angle Substitution Def. of  angles

  10. Theorem 4.2 If two angles are adjacent and supplementary, then they form a linear pair.

  11. Theorem 4.3 Angles that form a linear pair are supplementary.

  12. Theorem 4.4 If one angle of a linear pair is a right angle, then the other angle is also a right angle.

  13. Theorem 4.5 Vertical Angle Theorem. Vertical angles are congruent.

  14. Theorem 4.6 Congruent supplementary angles are right angles.

  15. Theorem 4.7 Angle Bisector Theorem. If AB bisects CAD, then mCAB = ½mCAD.

  16. Practice: If the mA = 58°, find the measure of the supplement of A.

  17. Practice: If the mA = 58°, find the measure of the complement of A.

  18. Practice: If the mA = 58°, find the measure of an angle that makes a vertical angle with A.

  19. Practice: If the mA = 58°, find the measure of an angle that makes a linear pair with A.

  20. Practice: If the mA = 58°, find the measures of the angles formed when A is bisected.

  21. Homework pp. 137-141

  22. A F G E B D C ►A. Exercises mAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°. 7. Name two pairs of supplementary angles.

  23. A F G E B D C ►A. Exercises mAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°. 9. What is mFGE?

  24. ►B. Exercises Give the reason for each step in the proofs below. 18-22. Theorem 4.3 Angles that form a linear pair are supplementary. Given:PAB and BAQ form a linear pair Prove: PAD and BAQ are supplementary

  25. ■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be? 41. Addition property of 

  26. ■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be? 42. Multiplication property of 

  27. ■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be? 43. Reflexive property of 

  28. ■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be? 44. Transitive property of 

  29. ■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be? 45. Why is  not an equivalence relation?

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