Sec. 1 – 2 Sec. 1 – 2 Points, Lines, & Points, Lines, &

PlanesPlanes

Objectives:Objectives:

1) Understand the basic terms of 1) Understand the basic terms of geometry.geometry.

2) Understand the basic postulates 2) Understand the basic postulates of geometry.of geometry.

3 Undefined Terms of 3 Undefined Terms of GeometryGeometry

PointPoint Is a location.Is a location. Represented by a small dot & by a Represented by a small dot & by a

capital letter.capital letter. Reads: Point AReads: Point A

A

3 Undefined Terms 3 Undefined Terms ContinuesContinues

LineLine Is a series of points that extend in two Is a series of points that extend in two

opposite directions w/o end.opposite directions w/o end. Defined by any two points on that line.Defined by any two points on that line. Name a line by 2 capital letters or 1 lower Name a line by 2 capital letters or 1 lower

case letter.case letter. Points that lie on the same line are called Points that lie on the same line are called

Collinear Collinear Points.Points. Notation is important: AB or line tNotation is important: AB or line t

A B

tC

AC BC

CA BA

The last of the Undefined The last of the Undefined TermsTerms

PlanePlane A flat surface that extends indefinitelyA flat surface that extends indefinitely Contains lines and pointsContains lines and points Named by 3 Noncollinear points or by a Named by 3 Noncollinear points or by a

capital script letter.capital script letter. Points & lines in the same plane are Points & lines in the same plane are

coplanar.coplanar. Notation: PQR or Plane Notation: PQR or Plane RR

Q P

R R

Space Space – Is defined as the set of all points– Is defined as the set of all points

Ex.1: Name some planes Ex.1: Name some planes and lines.and lines.

A B

C D

E

FG

H

Use the figure below. Name all segments that

are parallel to AE. Name all segments that are skew to AE.

Parallel segments lie in the same plane, and the lines that contain them do not intersect. The three segments in the figure above that are parallel to AE are BF, CG, and DH.

Skew lines are lines that do not lie in the same plane. The four lines in the figure that do not lie in the same plane as AE are BC, CD, FG, and GH.

A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

PostulatePostulate – Is an accepted – Is an accepted statement of fact.statement of fact. Aka: Aka: AxiomAxiom

P(1 – 1) Through any two points P(1 – 1) Through any two points there is exactly one line.there is exactly one line.

P(1 – 2) If two lines intersect, then P(1 – 2) If two lines intersect, then they intersect in exactly one point.they intersect in exactly one point.

k

r

A

P(1 – 3) If two planes intersect, then P(1 – 3) If two planes intersect, then they intersect in exactly one line.they intersect in exactly one line.

P(1 – 4) Through any three P(1 – 4) Through any three noncollinear points there is exactly noncollinear points there is exactly one plane.one plane.

A B

C D

E

FG

H

Which plane contains the points: A, B, C

Which plane contains the points: F, B, E

Which plane contains the points: H, A, B

Points X, Y, and Z are the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior of the triangle formed by X, Y, and Z.

Shade the plane that

contains X, Y, and Z.