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Do First

Do First. Complementary angles add up to 90 º. 30 º. 40 º. 50 º. 60 º. Adjacent and Complementary Angles. Complementary Angles but not Adjacent. Supplementary Angles sum to 180 °. 150 °. 30 °. 2. Angle Relationships. Conjecture 2: Vertical Angles Conjecture

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Do First

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  1. Do First

  2. Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Anglesbut not Adjacent

  3. Supplementary Anglessum to 180° 150° 30°

  4. 2. Angle Relationships

  5. Conjecture 2: Vertical Angles Conjecture If two angles form vertical angles they are congruent. 2. Angle Relationships

  6. Conjecture 3: Linear Pair Conjecture If two angles form a linear pair then they are supplementary. 2. Angle Relationships

  7. Vertical Anglesare opposite one another.Vertical angles are congruent. 100° 100°

  8. Lines l and m are parallel.l||m Note the 4 angles that measure 120°. 120° 120° l 120° 120° m Line n is a transversal. n

  9. Lines l and m are parallel.l||m There are 4 pairs of angles that are vertical. There are many pairs of angles that are supplementary. 60° 120° 120° 60° l 60° 120° 120° 60° m Line n is a transversal. n

  10. Conjecture 4: Triangle Sum Conjecture The sum of the angles of a triangle is 180°. 2. Angle Relationships

  11. Conjecture 5: Parallel Line Conjecture If two parallel lines are cut by a transversal then: alternate interior angles are congruent, alternate exterior angles are congruent, and corresponding angles are congruent. 5. Angle Relationships

  12. If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

  13. 5. Angle Relationships How many angles are there? 1 2 8 3 4 Corresponding angles. 2 & 6 4 & 8 3 & 7 1 & 5 5 6 Alternate interior angles 7 8 4 & 5 3 & 6 Alternate exterior angles 1 & 8 2 & 7

  14. 5. Angle Relationships Conjecture 5: Parallel Line Conjecture If two parallel lines are cut by a transversal then: alternate interior angles are congruent, alternate exterior angles are congruent, and corresponding angles are congruent.

  15. 1) Find the missing angle. ?° 36°

  16. 1) Find the missing angle. ?° 36° 90 ° – 36 = 54°

  17. 2) Find the missing angle. ?° 64°

  18. 2) Find the missing angle. ?° 64° 90 ° – 64° = 26°

  19. 5) Find the missing angle. 168° ?°

  20. 5) Find the missing angle. 168° ?° 180° – 168° = 12°

  21. 6) Find the missing angle. ?° 58°

  22. 6) Find the missing angle. ?° 58° 180° – 58° = 122°

  23. 7) Solve for x. 5x 4x 4x + 5x = 180 9x = 180 x = 20

  24. 8) Solve for x. 3x + 20 2x + 10

  25. 9) Lines l and m are parallel.l||mFind the missing angles. 42° a ° c° b° l d° e° g° f° m

  26. 9) Lines l and m are parallel.l||mFind the missing angles. 42° 138° 138° 42° l 42° 138° 138° 42° m

  27. 10) Lines l and m are parallel.l||mFind the missing angles. 81° a ° c° b° l d° e° g° f° m

  28. 10) Lines l and m are parallel.l||mFind the missing angles. 81° 99° 99° 81° l 81° 99° 99° 81° m

  29. 11) Find the missing angles. 70 ° 70 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 65 °

  30. 11) Find the missing angles. 70 ° 70 ° 40° Hint: The 3 angles in a triangle sum to 180°. 75 ° 65 °

  31. 12) Find the missing angles. 45 ° 50 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 75 °

  32. 12) Find the missing angles. 45 ° 50 ° 85° Hint: The 3 angles in a triangle sum to 180°. 20° 75 °

  33. In the figure a || b. 13. Name the angles congruent to 3. 1, 5, 7 14. Name all the angles supplementary to 6. 1, 3, 5, 7 15. If m1 = 105° what is m3? 105° 16. If m5 = 120° what is m2? 60°

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