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Lesson 1 Menu

Warm-up Problems What is the value of x 2 + 3yz if x = 3, y = 6, and z = 4? Solve 2(x – 7) = 5x + 4. Is (–2, 5) a solution of 3x + 4y = 14? Factor 9x 2 – 25y 2 . Graph y = 3x + 2. Find all of the solutions of 2x 2 + 5x – 3 = 0. –3 only ½ and 3 –3 and ½ no solutions. Lesson 1 Menu.

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Lesson 1 Menu

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  1. Warm-up Problems • What is the value of x2 + 3yz if x = 3, y = 6, and z = 4? • Solve 2(x – 7) = 5x + 4. • Is (–2, 5) a solution of 3x + 4y = 14? • Factor 9x2 – 25y2. • Graph y = 3x + 2. • Find all of the solutions of 2x2 + 5x – 3 = 0. • –3 only • ½ and 3 • –3 and ½ • no solutions Lesson 1 Menu

  2. Identify and model points, lines, and planes. • Identify collinear and coplanar points and intersecting lines and planes in space. • undefined term • plane • coplanar • space • locus • point • line • collinear Lesson 1 MI/Vocab

  3. Lesson 1 KC1

  4. 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. Answer: The line can be named as line a. Lesson 1 Ex1

  5. Name Lines and Planes B. Use the figure to name a plane containing point L. 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 Lesson 1 Ex1

  6. 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. Lesson 1 Ex1

  7. Model Points, Lines, and Planes A. Name the geometric shape modeled by a 10  12 patio. Answer: The patio models a plane. Lesson 1 Ex2

  8. Model Points, Lines, and Planes B. Name the geometric shape modeled by a water glass on a table. Answer: The glass on the table models a point on a plane. Lesson 1 Ex2

  9. Draw Geometric Figures Draw a surface to represent plane R and label it. Lesson 1 Ex3

  10. Draw Geometric Figures Draw a line anywhere on the plane. Lesson 1 Ex3

  11. Draw Geometric Figures Draw dots on the line for point A and B. Label the points. Lesson 1 Ex3

  12. Draw Geometric Figures Lesson 1 Ex3

  13. Draw Geometric Figures Draw dots on this line for point D and E. Label the points. Lesson 1 Ex3

  14. Draw Geometric Figures Label the intersection point of the two lines as P. Lesson 1 Ex3

  15. Draw Geometric Figures Answer: Lesson 1 Ex3

  16. 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). Lesson 1 Ex3

  17. Interpret Drawings A. How many planes appear in this figure? Answer: There are two planes: plane S and plane ABC. Lesson 1 Ex4

  18. Interpret Drawings B. Name three points that are collinear. Answer: Points A, B, and D are collinear. Lesson 1 Ex4

  19. 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. Lesson 1 Ex4

  20. Interpret Drawings Answer: The two lines intersect at point A. Lesson 1 Ex4

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