LESSON 1.1 Points, Lines and Planes Objective: I will be able to… 1.Identify and model points, lines, and planes as well as intersecting lines and planes 2.Make generalizations about geometric properties

LESSON Undefined Terms Line: made of points that extend in one dimension – no width or depth, but infinite length. 2 points determine a line. AB l line l Point: a location with no dimensions. Usually represented by a dot and a capital letter. A pt A

LESSON Plane: made of points that extend infinitely in two directions, but has no height. A flat surface with no thickness. Three noncollinear points determine and name a plane. A capital script letter can also name a plane. D C B A M

LESSON Defined Term: items defined by means of undefined terms or previously defined terms. Collinear: points or other objects that all lie on one line. AB C D D

LESSON Defined Term: items defined by means of undefined terms or previously defined terms. Coplanar: points or other objects that all lie on one plane. D C B A M

LESSON Example 1 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 Example 1 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. There are 15 different three-letter names for this plane (any order)

LESSON Example 1a A. Use the figure to name a line containing the point X. Line c B. Use the figure to name a plane containing point Z. Plane P

LESSON Example 2 A. Name the geometric shape modeled by a 10  12 patio. Answer: The patio models a plane. LESSON

Example 2a Point A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city.

LESSON Example 2b Plane B. Name the geometric shape modeled by the ceiling of your classroom.

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Example 3 Draw a surface to represent plane R and label it.

LESSON Example 3 Draw a line anywhere on the plane.

LESSON Example 3 Draw dots on the line for point A and B. Label the points.

LESSON Example 3

LESSON Example 3 Draw dots on this line for point D and E. Label the points.

LESSON Example 3 Label the intersection point of the two lines as P.

LESSON Example 3 Answer:

LESSON A.B. C.D. Example 3a A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines.

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

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

LESSON Try on your own! Refer to the figure. How many planes are shown in the figure? How many of the planes contain points F and E? Name four points that are coplanar. Are points A, B, and C coplanar? Explain.

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What is this?

LESSON What is this?

LESSON What is this? ABC

LESSON Undefined term: a term that is only explained using examples and descriptions Point: a location with no dimensions; it has no shape or size Line: made up of points and has no thickness or width (1 dimension); must have 2 points for a line Plane: a flat surface made up of points that extends infinitely in all directions (2 dimensions); must have 3 non-collinear points for a plane

LESSON Collinear: points that lie on the same line Coplanar: points that lie on the same plane Intersection: the set of points they have in common What do 2 intersecting lines have in common? What do 2 intersecting planes have in common? What do an intersecting line and a plane have in common? Defined term: explained using undefined terms and/or other defined terms