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Warm Up

Warm Up. Given: Angle MOR = (3x + 7)° Angle ROP = (4x – 1)° MO OP Which angle is larger, angle MOR or angle ROP?. M. R. O. P. Complementary and Supplementary Angles. I CAN… Define and identify complementary and supplementary angles

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Warm Up

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  1. Warm Up • Given: Angle MOR = (3x + 7)° • Angle ROP = (4x – 1)° • MO OP • Which angle is larger, angle MOR or angle ROP? M R O P

  2. Complementary and Supplementary Angles I CAN… • Define and identify complementary and supplementary angles • Write proofs involving complementary and supplementary angles

  3. Complementary Angles • Two angles whose sum is 90 • A is complementary to B • JOC is the complement of COB B 38 52 A J C O B

  4. Supplementary Angles • Two angles whose sum is 180 • A is supplementary to B • HAM is the supplement of HAB B 64 116 A H M A B

  5. Definitions: If-then Form • If two angles form a right angle, then they are complementary. • If two angles form a straight angle, then they are supplementary.

  6. Example 1 • Given: TVK is a right  • Prove: 1 is comp. to 2 1 2 Statement Reason T X V K

  7. Example 2 • Given: Diagram as shown • Prove: 1 is supp. to 2 1 2 Statement Reason A B C

  8. Example 3 • The measure of one of two complementary angles is three greater than twice the measure of the other. Find the measure of each.

  9. Example 4 • The measure of the supplement of an angle is 60 less than 3 times the measure of the complement of the angle. Find the measure of the complement.

  10. Groups of 2 • Work with your partner to complete the proof I give you. • Write a paragraph proof. • Be prepared to present your proof to the class!!

  11. 1 3 • Given: 1 is supp. to 2 3 is supp. to 2 • Prove: 1  3 Write a paragraph proof: 2

  12. 1 3 • Given: 1 is comp. to 2 3 is comp. to 2 • Prove: 1  3 Write a paragraph proof: 2

  13. A B D C • Given: A is supp. to B C is supp. to D B  D • Prove: A  C Write a paragraph proof:

  14. A B D C • Given: A is comp. to B C is comp. to D B  D • Prove: A  C Write a paragraph proof:

  15. Theorem • If two angles are supplementary to the same angle, then they are congruent. • If 1 is supp. to 2 and 3 is supp. to 2, then 1  3. 1 3 2

  16. A Theorem B D C • If two angles are supplementary to congruent angles, then they are congruent. • If A is supp. to B, C is supp. to D, and B  D. then A  C.

  17. Theorem 1 3 • If two angles are complementary to the same angle, then they are congruent. • If 1 is comp. to 2 and 3 is comp. to 2, then 1  3. 2

  18. A Theorem B D C • If two angles are complementary to congruent angles, then they are congruent. • If A is comp. to B, C is comp. to D, and B  D, then A  C.

  19. Homework • p. 69 # 7 – 13, 16, 17, 21 • Read Sample Problems on pages 77 & 78 • p. 79 #1 - 9, 11, 14

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