Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

1.2 points, lines and planes

984 views

Published on

LINE, Point and PLANE

  • Be the first to comment

1.2 points, lines and planes

  1. 1. 5-1 Points, Lines, Planes, and Angles 5-1 Points, Lines, Planes, and Angles Warm Up Problem of the Day Lesson PresentationPre-AlgebraPre-Algebra
  2. 2. 5-1 Points, Lines, Planes, and Angles Warm Up Solve. 1. x + 30 = 90 x = 60 2. 103 + x = 180 x = 77 3. 32 + x = 180 x = 148 4. 90 = 61 + x x = 29 5. x + 20 = 90 x = 70Pre-Algebra
  3. 3. 5-1 Points, Lines, Planes, and Angles Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, 1 of the class wants sausage on the 3 pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza? 1 6Pre-Algebra
  4. 4. 5-1 Points, Lines, Planes, and Angles Learn to classify and name figures.Pre-Algebra
  5. 5. 5-1 Points, Lines, Planes, and Angles Vocabulary point line plane segment ray angle right angle acute angle obtuse angle complementary angles supplementary angles vertical angles congruentPre-Algebra
  6. 6. 5-1 Points, Lines, Planes, and Angles Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.Pre-Algebra
  7. 7. 5-1 Points, Lines, Planes, and Angles A point names a •A Point A location.Pre-Algebra
  8. 8. 5-1 Points, Lines, Planes, and Angles A line is perfectly C straight and l extends forever in B line l, or BC both directions.Pre-Algebra
  9. 9. 5-1 Points, Lines, Planes, and Angles A plane is a perfectly flat P E surface that D plane P, or F plane DEF extends forever in all directions.Pre-Algebra
  10. 10. 5-1 Points, Lines, Planes, and Angles A segment, or H line segment, is the part of a line GH between two G points.Pre-Algebra
  11. 11. 5-1 Points, Lines, Planes, and Angles A ray is a part of J a line that starts at one point and KJ extends forever in K one direction.Pre-Algebra
  12. 12. 5-1 Points, Lines, Planes, and AnglesAdditional Example 1A & 1B: Naming Points, Lines, Planes, Segments, and Rays A. Name 4 points in the figure. Point J, point K, point L, and point M B. Name a line in the figure. KL or JK Any 2 points on a line can be used.Pre-Algebra
  13. 13. 5-1 Points, Lines, Planes, and AnglesAdditional Example 1C: Naming Points, Lines, Planes, Segments, and Rays C. Name a plane in the figure. Plane , plane JKL Any 3 points in the plane that form a triangle can be used.Pre-Algebra
  14. 14. 5-1 Points, Lines, Planes, and AnglesAdditional Example 1D & 1E: Naming Points, Lines, Planes, Segments, and Rays D. Name four segments in the figure. JK, KL, LM, JM E. Name four rays in the figure. KJ, KL, JK, LKPre-Algebra
  15. 15. 5-1 Points, Lines, Planes, and Angles Try This: Example 1A & 1B A. Name 4 points in the figure. Point A, point B, point C, and point D B. Name a line in the figure. DA or BC Any 2 points on a line can be used. A B D CPre-Algebra
  16. 16. 5-1 Points, Lines, Planes, and Angles Try This: Example 1C C. Name a plane in the figure. Plane , plane ABC, Any 3 points in the plane BCD, plane CDA, plane that form a or plane DAB triangle can be used. A B D CPre-Algebra
  17. 17. 5-1 Points, Lines, Planes, and Angles Try This: Example 1D & 1E D. Name four segments in the figure AB, BC, CD, DA E. Name four rays in the figure DA, AD, BC, CB A B D CPre-Algebra
  18. 18. 5-1 Points, Lines, Planes, and Angles An angle (∠) is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees. 1 One degree, or 1°, is of a circle. m∠1 360 means the measure of ∠1. The angle can be named ∠XYZ, ∠ZYX, ∠1, or ∠Y. The vertex must be the middle letter. X 1 m∠1 = 50° Y ZPre-Algebra
  19. 19. 5-1 Points, Lines, Planes, and Angles The measures of angles that fit together to form a straight line, such as ∠FKG, ∠GKH, and ∠HKJ, add to 180°. G H F K JPre-Algebra
  20. 20. 5-1 Points, Lines, Planes, and Angles The measures of angles that fit together to form a complete circle, such as ∠MRN, ∠NRP, ∠PRQ, and ∠QRM, add to 360°. P N R Q MPre-Algebra
  21. 21. 5-1 Points, Lines, Planes, and Angles A right angle measures 90°. An acute angle measures less than 90°. An obtuse angle measures greater than 90° and less than 180°. Complementary angles have measures that add to 90°. Supplementary angles have measures that add to 180°.Pre-Algebra
  22. 22. 5-1 Points, Lines, Planes, and Angles Reading Math A right angle can be labeled with a small box at the vertex.Pre-Algebra
  23. 23. 5-1 Points, Lines, Planes, and Angles Additional Example 2A & 2B: Classifying Angles A. Name a right angle in the figure. ∠TQS B. Name two acute angles in the figure. ∠TQP, ∠RQSPre-Algebra
  24. 24. 5-1 Points, Lines, Planes, and Angles Additional Example 2C: Classifying Angles C. Name two obtuse angles in the figure. ∠SQP, ∠RQTPre-Algebra
  25. 25. 5-1 Points, Lines, Planes, and Angles Additional Example 2D: Classifying Angles D. Name a pair of complementary angles. ∠TQP, ∠RQS m∠TQP + m∠ RQS = 47° + 43° = 90°Pre-Algebra
  26. 26. 5-1 Points, Lines, Planes, and Angles Additional Example 2E: Classifying Angles E. Name two pairs of supplementary angles. ∠TQP, ∠RQT m∠TQP + m∠RQT = 47° + 133° = 180° ∠SQP, ∠RQS m∠SQP + m∠RQS = 137° + 43° = 180°Pre-Algebra
  27. 27. 5-1 Points, Lines, Planes, and Angles Try This: Example 2A A. Name a right angle in the figure. ∠BEC C B A 90° D 15° 75° EPre-Algebra
  28. 28. 5-1 Points, Lines, Planes, and Angles Try This: Example 2B & 2C B. Name two acute angles in the figure. ∠AEB, ∠CED C. Name two obtuse angles in the figure. ∠BED, ∠AEC C B A 90° D 15° 75° EPre-Algebra
  29. 29. 5-1 Points, Lines, Planes, and Angles Try This: Example 2D D. Name a pair of complementary angles. ∠AEB, ∠CED m∠AEB + m∠CED = 15° + 75° = 90° C B A 90° D 15° 75° EPre-Algebra
  30. 30. 5-1 Points, Lines, Planes, and Angles Try This: Example 2D & 2E E. Name two pairs of supplementary angles. ∠AEB, ∠BED m∠AEB + m∠BED = 15° + 165° = 180° ∠CED, ∠AEC m∠CED + m∠AEC = 75° + 105° = 180° C B A 90° D 15° 75° EPre-Algebra
  31. 31. 5-1 Points, Lines, Planes, and Angles Congruent figures have the same size and shape. • Segments that have the same length are congruent. • Angles that have the same measure are congruent. • The symbol for congruence is ≅, which is read “is congruent to.” Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.Pre-Algebra
  32. 32. 5-1 Points, Lines, Planes, and Angles Additional Example 3A: Finding the Measure of Vertical Angles In the figure, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles. A. If m∠1 = 37°, find m∠ 3. The measures of ∠1 and ∠2 add to 180° because they are supplementary, so m∠2 = 180° – 37° = 143°. The measures of ∠2 and ∠3 add to 180° because they are supplementary, so m∠3 = 180° – 143° = 37°.Pre-Algebra
  33. 33. 5-1 Points, Lines, Planes, and Angles Additional Example 3B: Finding the Measure of Vertical Angles In the figure, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles. B. If m∠4 = y°, find m∠2. m∠3 = 180° – y° m∠2 = 180° – (180° – y°) = 180° – 180° + y° Distributive Property = y° m∠2 = m∠4Pre-Algebra
  34. 34. 5-1 Points, Lines, Planes, and Angles Try This: Example 3A In the figure, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles. 2 A. If m∠1 = 42°, find m∠3. 3 1 4 The measures of ∠1 and ∠2 add to 180° because they are supplementary, so m∠2 = 180° – 42° = 138°. The measures of ∠2 and ∠3 add to 180° because they are supplementary, so m∠3 = 180° – 138° = 42°.Pre-Algebra
  35. 35. 5-1 Points, Lines, Planes, and Angles Try This: Example 3B In the figure, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles. 2 B. If m∠4 = x°, find m∠2. 3 1 4 m∠3 = 180° – x° m∠2 = 180° – (180° – x°) = 180° –180° + x° Distributive Property = x° m∠2 = m∠4Pre-Algebra
  36. 36. 5-1 Points, Lines, Planes, and Angles Lesson Quiz In the figure, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles. 1. Name three points in the figure. Possible answer: A, B, and C 2. Name two lines in the figure. Possible answer: AD and BE 3. Name a right angle in the figure. Possible answer: ∠AGF 4. Name a pair of complementary angles. Possible answer: ∠1 and ∠2 5. If m∠1 = 47°, then find m∠ 3. 47°Pre-Algebra

×