1.2 Points, Lines, and Planes the 3 undefined terms of Geometry

A Point No size, no dimensions, it only has position A true point cannot be seen with the naked eye Name a point with a capital letter. A Note the dot is only a representation of a pt.

l Read Line AB or Line l Line An infinite number of points that extends in 2 directions Name a line with 2 points(2 capital letters) Or with one lower case letter l Read Line AB or Line l

limited number, terminates Collinear points points on the same line Infinite never ending, ongoing Finite limited number, terminates Collinear points points on the same line Noncollinear points points not on the same line

Plane A flat surface without thickness that extends infinitely in all directions Name a plane with one capital letter that has no point or with 3 noncollinear points E Plane F, Plane ABC, Plane BAC, Plane DAC or Plane CBA , etc D

Coplanar points Points that lie in the same plane Noncoplanar points points that do not lie in the same plane

Postulate or Axiom A statement that we assume is true or that we accept as fact Theorem A statement that must be proven true. You use definitions, postulates and other theorems to prove theorems true.

Basic Postulates 2 points determine a line. 2 lines intersect in a point 2 planes intersect in a line 3 planes intersect in a point or a line If 2 pts lie in a plane, then the plane contains every pt on the line.

Rectangular Prism – faces are rectangles and bases are always parallel Diagram 1 Rectangular Prism – faces are rectangles and bases are always parallel

Parallel lines Coplanar lines that never intersect Skew lines Noncoplanar lines that never intersect

4 postulates 4 ways to determine a plane 3 noncollinear pts determine a plane A line and a pt not on the line determine a plane 2 ll lines determine a plane 2 intersecting lines determine a plane

Noncoplanar points and space are the same The set of all points Noncoplanar points and space are the same

4 noncoplanar points determine space Postulate 4 noncoplanar points determine space If you can make skew lines out of 4 pts, then you know you are in space.

Postulates An infinite number of planes can be passed through a line. Or a line determines an infinite number of planes.

Any 2 points are collinear Any three points lie in the same plane Only 3 noncollinear points determine one plane Skew lines always indicate space

R Give a reason for each answer!!!! A,B,C E,F,C,B G,D E,F,A G,C,A,B Determine if the following sets of points are collinear, noncollinear (coplanar), or noncoplanar (space). A,B,C E,F,C,B G,D E,F,A G,C,A,B F,C D,A,R R Give a reason for each answer!!!!

J Determine if the following are collinear, coplanar, or noncoplanar. E,D 5. A,C A,B,F 6. E,F,C,B G,C,B,A 7. B,D,E,H F,A,H,B 8. G,A 9. A, J, B

Postulate – the intersection of 2 planes is a line Plane SUY ∩ Plane CSY in SY Diagram 2

Explain the relationship between 2 planes. They intersect in a line or they are parallel. Diagram 3

Give the intersection of the following: Diagram 3 Give the intersection of the following: Plane UXV ∩ Plane UXQ Plane UQR ∩ Plane XWS Plane VWS ∩ Plane XUV

Explain the relationship between a line and a plane. They intersect in a pt or a line. Diagram 4

Distribute Geometry Plane and Simple worksheet # 5 Allow students to work together for about 5 to 10 minutes

Hapless Hairline True/False A plane is determined by 2 intersecting lines. If 3 pts are coplanar, they are collinear. Any 2 pts are collinear. A plane and a line intersect at most in one pt.

3 points are not always coplanar. 2 planes intersect in infinitely many pts. 2 different planes intersect in a line. A line lies in one and only one plane. A line and a pt not on the line lie in one and only one plane. 3 planes can intersect in only one pt.

11. 3 lines can intersect in only one pt. 3 lines can intersect in only 2 points. The intersection of any 2 half-planes is necessarily a half-plane. The edge of a half-plane is another half-plane.

assign pgs. 13-15 ( 1-51 odd), (60-66 all) hw

Diagram 1

Diagram 2

Diagram 3

Diagram 4