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Improve your math problem-solving skills by learning about lines, planes, and geometric shapes. Practice identifying points, lines, and planes, and understand their relationships.

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  1. Splash Screen

  2. 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

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

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

  5. 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

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

  7. 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

  8. 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

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

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

  11. Concept

  12. 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

  13. 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

  14. 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

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

  16. 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

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

  18. 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

  19. 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

  20. 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

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

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

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

  24. Draw Geometric Figures Example 3

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

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

  27. Draw Geometric Figures Answer: Example 3

  28. Draw Geometric Figures Answer: Example 3

  29. 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

  30. 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

  31. 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

  32. Example 3b

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

  34. Interpret Drawings A. How many planes appear in this figure? Answer: There are two planes: plane S and plane ABC. Example 4

  35. Interpret Drawings B. Name three points that are collinear. Answer: Points A, B, and D are collinear. Example 4

  36. Interpret Drawings C. Are points A, B, C, and D coplanar? Explain. Answer: Points A, B, C, and D all lie in plane ABC, so they are coplanar. Example 4

  37. Interpret Drawings Answer: The two lines intersect at point A. Example 4

  38. A. How many planes appear in this figure? A. one B. two C. three D. four Example 4a

  39. B. Name three points that are collinear. A.B, O, and X B.X, O, and N C.R, O, and B D.A, X, and Z Example 4b

  40. C. Are points X, O, and R coplanar? A. yes B. no C. cannot be determined Example 4c

  41. A. point X B. point N C. point R D. point A Example 4d

  42. End of the Lesson

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