1.2 Points, Lines and Planes Geometry

Objectives/Assignment: Understand and use the basic undefined terms and defined terms of geometry. Sketch the intersections of lines and planes.

Using Undefined terms and definition A definition uses known words to describe a new word. In geometry, some words such as point, line and plane are undefined terms or not formally defined.

Example what your note page should look like now Name____________________________ Date___________________Period_____ Class_____________________________ 1.2 Points, Lines, & Planes Objectives: Assignment: Using undefined terms and definitions Understand and use the basic undefined terms and defined terms of geometry. Sketch the intersections of lines and planes. Assignment: pp. 13-15 #1-72 all A definition uses known words to describe a new word. In geometry, some words such as point, line and plane are undefined terms or not formally defined.

Using Undefined terms and definition A point has no dimension. It is usually represented by a small dot. A Point A

Using Undefined terms and definition A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. In this book, lines are always straight lines. l A B Line l or AB

Using Undefined terms and definition A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end even though the drawing of a plane appears to have edges. A B C M Plane M or plane ABC

A few basic concepts . . . Must be commonly understood without being defined. One such concept is the idea that a point lies on a line or a plane. Collinear points are points that lie on the same line. Coplanar points are points that lie on the same plane.

Ex. 1: Naming Collinear and Coplanar Points Name three points that are collinear Solution: D, E and F lie on the same line, so they are collinear. H G E F D

Ex. 1: Naming Collinear and Coplanar Points Name four points that are coplanar. Solution: D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn. H G E F D

Ex. 1: Naming Collinear and Coplanar Points Name three points that are not collinear. Solution: There are many correct answers. For instance, points H, E, and G do not lie on the same line. H G E F D

More . . . A B Ray AB The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie on the same side of A as point B. l B A Line l or AB

More . . . A B Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions. Ray BA l B A Line l or AB

More . . . If C is between A and B, then CA and CB are opposite rays. Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane. l B C A Line l or AB

Ex. 2: Drawing lines, segments and rays Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. Draw J, K and L Then draw JK J K L

Ex. 2: Drawing lines, segments and rays Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. K Draw KL J L

Ex. 2: Drawing lines, segments and rays Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. K Draw LJ J L

Ex. 3: Drawing Opposite Rays Draw two lines. Label points on the lines and name two pairs of opposite rays. Solution: Points M, N, and X are collinear and X is between M and N. So XM and XN are opposite rays. M Q X P N

Ex. 3: Drawing Opposite Rays Draw two lines. Label points on the lines and name two pairs of opposite rays. Solution: Points P, Q, and X are collinear and X is between P and Q. So XP and XQ are opposite rays. M Q X P N

Ex. 4: Sketching intersections Sketch the figure described. A line that intersects a plane in one point Draw a plane and a line. Emphasize the point where they meet. Dashes indicate where the line is hidden by the plane

Ex. 4: Sketching intersections Sketch the figure described. Two planes that intersect in a line Draw two planes. Emphasize the line where they meet. Dashes indicate where one plane is hidden by the other plane.

vocabulary A POINT is simply a location. A LINE is made up of points and has no thickness or width. Points on the same line are said to be COLLINEAR. A PLANE is a flat surface made up of points. Points that lie on the same plane are said to be COPLANAR. A plane has no depth and extends infinitely in all directions. Points are often used to name lines and planes.

Review Concept Model A Drawn As a dot Facts Point A B A n point line plane B Model A A A R S K n Drawn As a shaded slanted 4-sided figure As a dot Line with arrowhead at each end Two letters representing two points on the line, or a lowercase script letter Named by Three none collinear points or a capital script letter A capital letter Facts A point has neither shape nor size There is exactly one plane through any 3 noncollinear points. There is exactly one line through any two points K Words / Symbols Point A Line n, line AB or line BA Plane , plane RAS,plane SAR, plane ARS, any combo Of the three letters.