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complementary_and_supplementary_angles.ppt
- 1. M.G. 2.1 Identifyangles as adjacent, vertical, complementary and supplementary. Objective-- Students will identify angles as complementary and supplementary and solve problems with an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.
- 2. Warm Up Identify thetype of angle. 1. 70° 2. 90° 3. 140° 4. 180° acute right obtuse straight
- 3. Vocabulary congruent vertical angles adjacent angles complementaryangles supplementary angles
- 4. Congruent angles havethe same measure. Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles
- 5. Adjacent angles areside by side and have a common vertex and ray. Adjacent angles may or may not be congruent. MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ.
- 6. Adjacent angles are“side by side” and share a common ray. 45º 15º
- 7. These are examplesof adjacent angles. 55º 35º 50º 130 º 80º 45º 85º 20º
- 8. These angles areNOT adjacent. 45º 55º 50º 100 º 35º 35º
- 9. When 2 linesintersect, they make vertical angles. 75º 75º 105 º 105 º
- 10. Vertical angles areopposite one another. 75º 75º 105 º 105 º
- 11. Vertical angles areopposite one another. 75º 75º 105 º 105 º
- 12. Vertical angles arecongruent (equal). 30º 150 º 150 º 30º
- 13. Supplementary angles addup to 180º. 60º 120º 40º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent
- 14. How can Iremember that? • Draw the S in Supplementary S • Since supplementary angles equal 180*, turn that S into a number 8 by drawing a line diagonal, then add a 1 in front of that and a 0 after to make it 180. • So you change the S in supplementary into 180*!! S S 1S0*
- 15. Complementary angles addup to 90º. 60º 30º 40º 50º Adjacent and Complementary Angles Complementary Angles but not Adjacent
- 16. How can Iremember that? • Draw the C in Complementary C • Since complementary angles equal 90*, turn that C into a number 9 by drawing a line, then add a 0 after that to make it 90. • So you change the C in complementary into 90*!! C C C
- 17. Remember our Objective… Studentswill identify angles as complementary and supplementary and solve problems with an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.
- 18. Remember: Two anglesare supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other. 1 2 20 160 These are supplements of each other because their angles add up to 180.
- 19. 3 STEPS forFinding Missing Angles: 1) First, create an addition equation by adding both angles. 1) The sum of the two angles will equal 90° for Complementary Angles and 180° for Supplementary Angles. 3) Solve the equation using the inverse rules!
- 20. x Example 1 Findthe value of x by making an equation. x + = 180 20 x = 160 20
- 21. x Example 2 Findthe value of x by writing your equation. 65 x + = 180 65 x = 115
- 22. Two angles arecomplementary if the sum of their measures is 90 degrees. Each angle is the complement of the other. 1 2 30 60 These are complements of each other because their angles add up to be 90.
- 23. Example 3 Findthe value of x. x 15 x + = 90 15 x = 75
- 24. 1 2 3 5 Are angles 4and 5 supplementary angles? Are angles 2 and 3 complementary angles? Are angles 2 and 1 complementary angles? Are angles 4 and 3 supplementary angles? no no yes yes Now, think of what we talked about today. 4
- 25. Example 4 Findthe value of x. (4x + 3) (x - 8) (4x + 3) + (x - 8) = 90 x = 19 5x - 5 = 90 5x = 95
- 26. Example 5 Findthe value of x. (7x 10) 3x (7x + 10) + 3x = 180 10x + 10 = 180 10x = 170 x = 17
- 27. 1 2 3 5 Are angles 1and 2 a linear pair? Are angles 1 and 3 adjacent angles? Are angles 2 and 3 adjacent angles? Are angles 3 and 4 a linear pair? no no yes yes Think back to last class… 4
- 28. Remember…Students will identify anglesas complementary and supplementary and solve problems with an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.
- 29. Figure 1find themissing angles you may use a protractor to draw it! X Z Q S T V Y 40 50 40 R S
Editor's Notes
- #20 This is on p. 16 of the Study Guide problem #2.
- #21 This is on p. 16 of the Study Guide problem #3.
- #23 This is on p. 16 of the Study Guide problem #1.
- #25 This is on p. 16 of the Study Guide problem #6.
- #26 This is on p. 16 of the Study Guide problem #3.
- #29 This is the 2nd figure in the practice workbook p.16