Lesson 1 – 1 Points, Lines, and Planes Geometry Lesson 1 – 1 Points, Lines, and Planes Objective: Identify and model points, lines, and planes. Identify intersecting lines and planes.

Undefined terms Undefined terms: objects that are only explained using examples and descriptions. Point Line Plane

Point Point: Named: Example A point is a location. Has neither shape nor size Named: Capital letter Example Point A

Line Line: Named: Example Made up of points Has no thickness or width Exactly one line through and two points. Named: Any 2 points on the line (2 capital letters) Lowercase script letter Example line m or

Plane Plane: Named Example K A flat surface made up of points that extends infinitely in all directions. Exactly one plane through any 3 points not on the same line. Named Capital Script letter 3 points on the plane not on a line (3 capital letters) Example K Plane BCD (any order)

Definitions Collinear: Noncollinear: Coplanar Noncoplanar Points that lie on the same line Noncollinear: Points that do not lie on the same line. Coplanar Points that lie in the same plane Noncoplanar Points that do not line in the same plane

Use the figure to name each of the following: A line containing point W A plane containing point X Any one of the following work: Any one of the following work: (3 letters that are noncollinear) P, plane XZY, plane VZY, plane VZW, plane WZX, plane VZX, Plane WZY

Example Name the geometric term modeled by the objects in the picture. Push pin Maroon boarder The card itself Stripes on a sweater Corner of a box Point G Sample: plane FGJ lines point

Intersection Intersection of two or more geometric figures is the set of points they have in common. Where do two lines intersect? Where do two planes intersect? At a point. At a line

Draw the following intersects plane T at point S. Sample answer Must have the dashed line to show that the line goes through the plane and is not on or in the plane.

Draw the following Line p lies in plane N and contains point L. Sample answer.

Definitions Definitions are defined terms that are explained using undefined terms and/or other defined terms. Space: defined as a boundless, three-dimensional set of all points. Space can contain lines and planes.

Name 3 points that are collinear. How many planes appear in this figure. Name 3 points that are collinear. Name the intersection of plane HDG with plane X. At what point do LM and EF intersect? Explain. 6 planes: 5 around the pyramid and one on bottom of the the pyramid… don’t name the bottom plane twice. Points J, K, and D Make sure you have commas otherwise it names a plane. Don’t appear to intersect since L is the only point on line LM in the plane.

No, not all on the same plane. Are points E, D, F, and G coplanar? At what point or in what line do planes JDH, JDE, and EDF intersect? No, not all on the same plane. Point D is the only thing in common.

Homework Pg. 8 1 – 12 all, 14 – 46 EOE, 52, 66 – 82 EOE