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Learn about lines, planes, and points and how to draw and interpret geometric figures. Solve problems using basic geometric concepts and properties.

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  1. Splash Screen

  2. Five-Minute Check CCSS Then/Now New Vocabulary Key Concept: Undefined Terms Example 1: Name Lines and Planes Example 2: Real-World Example: Model Points, Lines, and Planes Example 3: Draw Geometric Figures Example 4: Interpret Drawings Lesson Menu

  3. What is the value ofx2 +3yz if x = 3, y = 6, and z = 4? A. 27 B. 33 C. 72 D. 81 5-Minute Check 1

  4. What is the value ofx2 +3yz if x = 3, y = 6, and z = 4? A. 27 B. 33 C. 72 D. 81 5-Minute Check 1

  5. A.–6 B. C.2 D.6 Solve 2(x – 7) = 5x + 4. 5-Minute Check 2

  6. A.–6 B. C.2 D.6 Solve 2(x – 7) = 5x + 4. 5-Minute Check 2

  7. Which is a solution of 3x + 4y = 14? A. (–3, 4) B. (–2, 5) C. (1, 3) D. (2, 3) 5-Minute Check 3

  8. Which is a solution of 3x + 4y = 14? A. (–3, 4) B. (–2, 5) C. (1, 3) D. (2, 3) 5-Minute Check 3

  9. Factor 9x2 – 25y2. A. (3x – 5y)2 B. (3x + 5y)2 C. (3x + 5y)(3x – 5y) D. (9x + 5y)(x – 5y) 5-Minute Check 4

  10. Factor 9x2 – 25y2. A. (3x – 5y)2 B. (3x + 5y)2 C. (3x + 5y)(3x – 5y) D. (9x + 5y)(x – 5y) 5-Minute Check 4

  11. A. B. C. D. Graph y = 3x + 2. 5-Minute Check 5

  12. A. B. C. D. Graph y = 3x + 2. 5-Minute Check 5

  13. Which of the following equations is a quadratic equation? A. 4x = 2 B. 5x + 2y = 13 C. 6x2 – 3x = 16 D. 5x3 – x2 + 2 = 0 5-Minute Check 6

  14. Which of the following equations is a quadratic equation? A. 4x = 2 B. 5x + 2y = 13 C. 6x2 – 3x = 16 D. 5x3 – x2 + 2 = 0 5-Minute Check 6

  15. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Mathematical Practices 4 Model with mathematics. 6 Attend to precision. CCSS

  16. You used basic geometric concepts and properties to solve problems. • Identify and model points, lines, and planes. • Identify intersecting lines and planes. Then/Now

  17. definition • defined term • space • undefined term • point • line • plane • collinear • coplanar • intersection Vocabulary

  18. Concept

  19. Answer: Name Lines and Planes A. Use the figure to name a line containing point K. Example 1

  20. Answer: The line can be named as line a. There are three points on the line. Any two of the points can be used to name the line. Name Lines and Planes A. Use the figure to name a line containing point K. Example 1

  21. Answer: Name Lines and Planes B. Use the figure to name a plane containing point L. Example 1

  22. Answer: The plane can be named as plane B. You can also use the letters of any three noncollinearpoints to name the plane.plane JKM plane KLM plane JLM Name Lines and Planes B. Use the figure to name a plane containing point L. Example 1

  23. Name Lines and Planes The letters of each of these names can be reordered to create other acceptable names for this plane. For example, JKM can also be written as JMK, MKJ, KJM, KMJ, and MJK. There are 15 different three-letter names for this plane. Example 1

  24. A.line X B.line c C.line Z D. A. Use the figure to name a line containing the point X. Example 1a

  25. A.line X B.line c C.line Z D. A. Use the figure to name a line containing the point X. Example 1a

  26. B. Use the figure to name a plane containing point Z. A.plane XY B.plane c C.plane XQY D.plane P Example 1b

  27. B. Use the figure to name a plane containing point Z. A.plane XY B.plane c C.plane XQY D.plane P Example 1b

  28. Model Points, Lines, and Planes A. Name the geometric shape modeled by a 10  12 patio. Answer: Example 2

  29. Model Points, Lines, and Planes A. Name the geometric shape modeled by a 10  12 patio. Answer: The patio models a plane. Example 2

  30. Model Points, Lines, and Planes B. Name the geometric shape modeled by a button on a table. Answer: Example 2

  31. Model Points, Lines, and Planes B. Name the geometric shape modeled by a button on a table. Answer: The button on the table models a point on a plane. Example 2

  32. A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city. A. point B. line segment C. plane D. none of the above Example 2a

  33. A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city. A. point B. line segment C. plane D. none of the above Example 2a

  34. B. Name the geometric shape modeled by the ceiling of your classroom. A. point B. line segment C. plane D. none of the above Example 2b

  35. B. Name the geometric shape modeled by the ceiling of your classroom. A. point B. line segment C. plane D. none of the above Example 2b

  36. Draw Geometric Figures Draw a surface to represent plane R and label it. Example 3

  37. Draw Geometric Figures Draw a line anywhere on the plane. Example 3

  38. Draw Geometric Figures Draw dots on the line for point A and B. Label the points. Example 3

  39. Draw Geometric Figures Example 3

  40. Draw Geometric Figures Draw dots on this line for point D and E. Label the points. Example 3

  41. Draw Geometric Figures Label the intersection point of the two lines as P. Example 3

  42. Draw Geometric Figures Answer: Example 3

  43. Draw Geometric Figures Answer: Example 3

  44. Draw Geometric Figures Answer: There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0). Example 3

  45. Draw Geometric Figures Answer: There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0). Example 3

  46. A. B.C.D. A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines. Example 3a

  47. A. B.C.D. A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines. Example 3a

  48. Example 3b

  49. A. B. C.D. Example 3b

  50. A. B. C.D. Example 3b

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