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Chapter 2.8

Chapter 2.8. Proving Angle Relationships. Concept. Concept. Use the Angle Addition Postulate. Prove that the m<1 = 89 , if m<2 = 56 and m<JKL = 145. J. K. 2. 1. L. Example 1. Prove that the m  1 = 104 if m  2 = 58 and m  JKL = 162. Concept. Concept. Example 2.

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Chapter 2.8

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  1. Chapter 2.8 Proving Angle Relationships

  2. Concept

  3. Concept

  4. Use the Angle Addition Postulate Prove that the m<1 = 89, if m<2 = 56 and m<JKL = 145. J K 2 1 L

  5. Example 1 Prove that the m1 = 104 if m2 = 58 and mJKL = 162.

  6. Concept

  7. Concept

  8. Example 2 QUILTINGThe diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD. A. 20 B. 30 C. 40 D. 50

  9. Concept

  10. Concept

  11. Concept

  12. Given: Prove: Example 3 Proofs Using Congruent Comp. or Suppl. Theorems

  13. Proof: Statements Reasons 1. m3 + m1 = 180;1 and 4 form a linear pair. 1. Given 2. 1 and 4 are supplementary. 2. Linear pairs are supplementary. 3. 3 and 1 are supplementary. 3. Definition of supplementary angles 4. 3  4 4. s suppl. to same  are . Example 3 Proofs Using Congruent Comp. or Suppl. Theorems

  14. Example 3 In the figure, NYR andRYA form a linear pair,AXY and AXZ form a linear pair, and RYA andAXZ are congruent. Prove that NYR and AXY are congruent.

  15. Statements Reasons 1. NYR and RYA, AXY and AXZ form linear pairs. 1. Given 2. NYR and RYA are supplementary. AXY and AXZ are supplementary. 2. If two s form a linear pair, then theyaresuppl.s. 3. Given 3. RYA  AXZ ? 4. ____________ 4.NYR  AXY Example 3 Which choice correctly completes the proof? Proof:

  16. Concept

  17. Proof: Statements Reasons Example 4 Use Vertical Angles If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step. 1. 1 and 2are vertical s. 1. Given

  18. A. B. C. D. Example 4

  19. Concept

  20. Try it! • Pg. 157 #22 - 26

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