Lesson 1 Menu Warm-up Problems 1.What is the value of x 2 + 3yz if x = 3, y = 6, and z = 4? 2.Solve 2(x – 7) = 5x + 4. 3.Is (–2, 5) a solution of 3x +

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

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

Lesson 1 KC1

Lesson 1 Ex1 Name Lines and Planes A. Use the figure to name a line containing point K. 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.

Lesson 1 Ex1 Name Lines and Planes B. Use the figure to name a plane containing point L. You can also use the letters of any three noncollinear points to name the plane. plane JKMplane KLMplane JLM Answer: The plane can be named as plane B.

Lesson 1 Ex1 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 Ex2 A. Name the geometric shape modeled by a 10  12 patio. Answer: The patio models a plane. Model Points, Lines, and Planes

Lesson 1 Ex2 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. Model Points, Lines, and Planes

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

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

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

Lesson 1 Ex3 Draw Geometric Figures

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

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

Lesson 1 Ex3 Draw Geometric Figures Answer:

Lesson 1 Ex3 Draw Geometric Figures There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0). Answer:

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

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

Lesson 1 Ex4 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. Interpret Drawings

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