1 2 Points Lines and Planes Using Undefined

1. 2 Points, Lines and Planes

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. l A B Line l or AB

Name that line

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 M C B Plane M or plane ABC

Name that Plane

A few basic concepts. . . n Collinear points are points that lie on the same line. n n n Non-Collinear points are points that do not lie on the same line. Coplanar points are points that lie on the same plane. Non-Coplanar points are points that lie on the same plane.

Ex. 1: Naming Collinear and Coplanar Points a. Name three points that are collinear H G D E F

Ex. 1: Naming Collinear and Coplanar Points b. H Name four points that are coplanar. G D E F

Ex. 1: Naming Collinear and Coplanar Points c. H Name three points that are not collinear. G D E F

More. . . n A The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. B Segment AB l B A Line l or AB

A More. . . n 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. B Ray AB l B A Line l or AB

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

More. . . n l If C is between A and B, then CA and CB are opposite rays. B C n 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. A Line l or AB

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

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

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

Ex. 3: Drawing Opposite Rays n Draw two lines. Label points on the lines and name two pairs of opposite rays. M Q X P N

Ex. 3: Drawing Opposite Rays n Draw two lines. Label points on the lines and name two pairs of opposite rays. M Q X P N

Ex. 4: Sketching intersections n a. Ø Ø Ø 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 n b. Ø Ø Ø 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.

Practice

Practice