6/1/ : Points, Lines and Planes 1-2: Points, Lines and Planes Expectations: 1.You will be able to identify points, lines and planes. 2.You will be able to correctly identify the figured formed by intersecting lines and planes.

6/1/ : Points, Lines and Planes A New Mathematical System Geometry is a system of mathematics. We will start from scratch and build the system as we go. Our system is based upon undefined terms and postulates and is built up using definitions and theorems.

6/1/ : Points, Lines and Planes Undefined Terms Undefined terms are terms that cannot be defined due to a lack of previously defined terms to use in the definitions.

6/1/ : Points, Lines and Planes Postulates Postulates are statements that are assumed to be true. We do not assume just anything, but rather statements that are obviously true. Just like undefined terms, postulates cannot be justified because we have to start somewhere.

6/1/ : Points, Lines and Planes Definitions Just like in English, definitions tell us exactly what an object is and when we know we have one.

6/1/ : Points, Lines and Planes Theorems A theorem is a mathematical statement that is proven to be true. Until a statement is proven, it is not a theorem.

6/1/ : Points, Lines and Planes Undefined Terms (Remember these!) There are 3 undefined terms in Geometry:

6/1/ : Points, Lines and Planes Point Points have ___ size and they mark exact locations. They are the most basic building block in geometry. Points are drawn as dots, just remember that in actuality points have no size. We name points with upper case letters. A

6/1/ : Points, Lines and Planes Line Lines are made up of points all strung together in a straight form. Lines have no width and they have ____________ length. Lines are named using 2 points from the line with a small line (double ended arrow) above the letters or a lower case script letter.

6/1/ : Points, Lines and Planes Name the line below in 3 ways A B l

6/1/ : Points, Lines and Planes Planes Planes are also made up of points. Planes have no thickness, are perfectly flat with infinite _______ and __________. Planes are named with upper case script letters or by listing 3 points from the plane (in any order) and are drawn as parallelograms (slanted rectangles)

6/1/ : Points, Lines and Planes Name the plane below in 3 different ways. A BC R

What geometric figure is said to be “one dimensional?” 6/1/ : Points, Lines and Planes

6/1/ : Points, Lines and Planes Space Defn: Space is the infinite set of all possible points. Space has infinite length, width and height.

6/1/ : Points, Lines and Planes Models A model is a figure that represents something else.

6/1/ : Points, Lines and Planes Models of 3 Undefined Terms Points:

6/1/ : Points, Lines and Planes Lines: Planes:

6/1/ : Points, Lines and Planes Collinear Points Defn: Three or more points are collinear iff (if and only if) they are ________________________. A B C A, B and C are collinear.

6/1/ : Points, Lines and Planes Non-Collinear Points Defn: Three or more points are non- collinear iff they are ____ collinear. X Y Z X, Y and Z are non-collinear.

6/1/ : Points, Lines and Planes Coplanar Points Defn: Four or more points are coplanar iff they are all contained on the _________ plane. E F G H E, F, G and H are coplanar.

6/1/ : Points, Lines and Planes Non-Coplanar Points Defn: Four or more points are non- coplanar iff they are not contained on the same plane. W, X, Y and Z are non-coplanar. W Y X Z

6/1/ : Points, Lines and Planes Uniqueness Postulate Through any __ distinct points there exists a unique line. Through any __ non-collinear points there exists a unique plane.

6/1/ : Points, Lines and Planes Flat Plane Postulate If two points of a line are contained in a plane, then the ____________________________ __________________.

6/1/ : Points, Lines and Planes Dimension Postulate Given a line in a plane, there is at least one point in the plane that is ______ on the line. Given a plane in space, there is at least one point in space ______ on the plane.

6/1/ : Points, Lines and Planes Intersection Postulate If two lines intersect, then their intersection is a _________. If two planes intersect, then their intersection is a __________.

6/1/ : Points, Lines and Planes Assignment pages 16-17, #19 – 33 (odds) and 43 – 51 (odds) Remember your assignment must be complete to receive credit.