Section 1 – Points, Lines, and Planes Geometry Section 1 – Points, Lines, and Planes

Example 1 Name Lines and Planes Example 2 Model Points, Lines, and Planes Example 3 Draw Geometric Figures Example 4 Interpret Drawings Lesson 1 Contents

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. Example 1-1a

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 noncollinear points to name the plane. plane JKM plane KLM plane JLM Example 1-1b

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 18 different three-letter names for this plane. Example 1-1c

Use the figure to name each of the following. a. a line containing point X b. a plane containing point Z Answer: line c, Answer: plane P, plane XYZ, plane ZYX, plane YZX, plane XZY, plane ZXY, plane YXZ Example 1-1d

Answer: The long hand on a clock models a line segment. VISUALIZATION Name the geometric shape modeled by the long hand on a clock. Answer: The long hand on a clock models a line segment. Example 1-2a

VISUALIZATION Name the geometric shape modeled by a 10  12 patio. Answer: The patio models a plane. Example 1-2b

VISUALIZATION Name the geometric shape modeled by the location where the corner of a driveway meets the road. Answer: The location where the corner of a driveway meets the road models a point. Example 1-2c

VISUALIZATION Name the geometric shape modeled by each object. a. a colored dot on a map used to mark the location of a city b. the ceiling of your classroom c. the railing on a stairway Answer: point Answer: plane Answer: line segment Example 1-2d

Draw a surface to represent plane R and label it. Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or . Draw a surface to represent plane R and label it. Example 1-3a

Draw a line anywhere on the plane. Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or . Draw a line anywhere on the plane. Example 1-3b

Draw and label a figure for the following situation Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or . B A Draw dots on the line for points A and B. Label the points. Example 1-3c

Draw and label a figure for the following situation Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or . B A Draw a line intersecting . Example 1-3d

Draw and label a figure for the following situation Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or . B A E D Draw dots on this line for points D and E. Label the points. Example 1-3e

Draw and label a figure for the following situation Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or . B A E D P Label the intersection point of the two lines as P. Example 1-3f

Draw and label a figure for the following situation. on a coordinate plane contains Q(–2, 4) and R(4, –4). Add point T so that T is collinear with these points. Draw and label a figure for the following situation. Graph each point and draw . 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 1-3h

Draw and label a figure for each relationship. a. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Add point F on plane D so that it is not collinear with any of the three given lines. Sample answer: Example 1-3i

Draw and label a figure for each relationship. b. on a coordinate plane contains B(–3, –2) and A(3, 2). Add point M so that M is collinear with these points. Sample answer: Example 1-3j

How many planes appear in this figure? Answer: There are two planes: plane S and plane ABC. Example 1-4a

Name three points that are collinear. Answer: Points A, B, and D are collinear. Example 1-4b

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 1-4c

At what point do and intersect? Answer: The two lines intersect at point A. Example 1-4d

a. How many planes appear in this figure? Answer: two Example 1-4e

b. Name three points that are collinear. Sample answer: A, X, and Z Example 1-4f

c. Are points X, O, and R coplanar? Explain. Answer: Points X, O, and R all lie in plane T, so they are coplanar. Example 1-4g

d. At what point do and intersect? Answer: R Example 1-4h