Lesson 1 1 Points Lines Planes Transparency 1

Lesson 1 -1 Points, Lines & Planes

Transparency 1 -1 5 -Minute Check on Algebra 1. 6 x + 45 = 18 – 3 x 2. x 2 – 45 = 4 3. (3 x + 4) + (4 x – 7) = 11 4. (4 x – 10) + (6 x +30) = 180 5. Find the slope of the line k. y k (6, 4) (0, 1) 6. (-6, -2) Find the slope of a perpendicular line to k Standardized Test Practice: A 1/2 B 2 C -1/2 D -2 Click the mouse button or press the Space Bar to display the answers. B A C x

Transparency 1 -1 5 -Minute Check on Algebra 1. 6 x + 45 = 18 – 3 x 9 x +45 = 18 2. x 2 – 45 = 4 x² = 49 3. (3 x + 4) + (4 x – 7) = 11 7 x - 3 = 11 4. (4 x – 10) + (6 x +30) = 180 10 x + 20 = 180 9 x = -27 x = √ 49 x = +/- 7 7 x = 14 x=2 10 x = 160 5. Find the slope of the line k. (0, 1) (-6, -2) Find the slope of a perpendicular line to k 1/2 B 2 C -1/2 D k (6, 4) Standardized Test Practice: A x = 16 y ∆y y 2 – y 1 4– 1 3 1 m = ----------- = ---∆x x 2 – x 1 6– 0 6 2 6. x = -3 -2 Click the mouse button or press the Space Bar to display the answers. B A ∆x ∆y C x

Objectives • Identify and model points, lines and planes • Identify collinear and coplanar points and intersecting lines and planes in space

Vocabulary • Point – a location in space; usually named by coordinate location (x, y) • Line segment – a collection of collinear points between two points • Line – a collection of points, defined by two points • Collinear – points on the same line are called collinear • Plane – flat surface made up of points; defined by at least three points (or two intersecting lines) • Coplanar – points lying on the same plane are called coplanar • Space – is a boundless, three dimensional set of all points

Geometric Definitions E F D S P R T Coordinate Plane Examples y A (0, 1) Line RS Line Segments RT and ST Rays DE and DF Angle: EDF Vertex: D (point) Points R, P, and S are collinear Points R, T, and S are not k x Point A or coordinates (0, 1) Line k X, Y coordinate plane (intersection of x and y coordinate axes)

Visual Definitions Points y A, B, C, D Line k Plane xy coordinate Coplanar A, B, C, D C (0, 1) A, B, C BA, BC, AC (6, 4) D Collinear Line Segments k (-5, 5) A (-6, -2) B x

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.

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 JKM plane KLM plane JLM

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

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

a. How many planes appear in this figure? Answer: two

b. Name three points that are collinear. Sample answer: A, X, and Z

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

Summary & Homework • Summary: – Two points determine a line – Three noncollinear points determine a plane • Homework: – pg 9, 10: 7 -8, 13, 15, 17, 22 -23, 32, 34 -35