1.3 Points, Lines, and Planes You will learn to identify and draw models of points, lines, and planes, and determine their characteristics. Pardekooper

Point: –a–a–a–a concept used to define an exact location in space - a point has no size - named using capital letters

Line: –a–a–a–an ideal zero-width, infinitely long, perfectly straight curve Pardekooper - made up of an infinite number of points. number of points.

Let’s try a problem. R T m S Name two points on line m. Possible answers:  point R and point S  point R and point T  point S and point T

Give three names for the line. Possible answers: NOTE: Any two points on the line or the script letter can be used to name it. Here’s another problem. R T m S RS, RT, ST or line m

Collinear points: –t–t–t–three or more points that lie in a straight line Pardekooper

R T S U V Name three points that are collinear. Possible answers:  points R, S, and point T  points U, S, and point V Just one more problem

Plane: –a–a two-dimensional surface that is perfectly flat. {three non-collinear points determine a plane} Pardekooper

Coplanar: –G–G–G–Geometric objects lying in a common plane usually a point and a line.

How about those Postulates 1-1: –G–Given two points, there is exactly one line that goes through the points.

How about those Postulates Pardekooper 1-2 –T–Two lines intersect in exactly one point

How about those Postulates Pardekooper 1-3 –T–Two planes intersect in exactly one line

How about those Postulates Pardekooper 1-4: –G–Given three non-colinear points, there is exactly one plane that goes through the points. --A plane can be named with a single uppercase script letter or by three noncollinear points. M

AA BB CC DD EE Name three points that are coplanar. Answers (may be others) A, B, & C or A, D, & E A few more problems

AA BB CC DD EE Name three points that are noncoplanar. Answers (may be others) D, A, & B B, A, & E D, A, & C C, A, & E A few more problems

AA BB CC DD EE Name a point that is in both planes. A A few more problems

Assignment Pardekooper

Are the following sets of points coplanar ? 1. AB and C2. B and F 3. EB and A4. F in plane Q 1.3 Points, Lines and Planes Geometry A  B C D E Q      F Find the intersection of the following lines and planes in the figure at the right 5. GK and LG6. DB and FC 7. F, A, B, and C8. FB and BD G H K J L M P N Refer to the diagram at the right. 9. What is the intersection of plane P and Q ? 10. Are A and C collinear ? 11. Are planes P and Q coplanar? Q P A B C D    