1.2 Points, Lines, and Planes 9/10/12• Geometry – a mathematical system built on

accepted facts, basic terms, and definitions.• Undefined Terms – the basic ideas that you can use

to build the definitions of all other figures in geometry.– You cannot define undefined terms, but it is important

to have a general description of their meanings.

Undefined Terms• Point – indicates a location and has no size.– Represent a point by a dot.– Name it with a capital letter, such as A.

• Line – represented by a straight path that extends in two opposite directions without end and has no thickness.– A line contains infinitely many points.– Can name a line by any two points on the line, or by a single

lowercase letter.• Plane – represented by a flat surface that extends

without end and has no thickness.– Contains infinitely many lines.– Can name a plane by a capital letter or by at least three

points in the plane that do not all lie on the same line.

Undefined Terms

Point A

line l or AB

plane P or plane ABC

Points

• Collinear points – points that lie on the same line.

• Coplanar points – points that lie in the same plane.– All the points of a line are coplanar.

Naming Points, Lines, and Planes• What are two other ways to name QT?• What are two other ways to name plane P?• What are the names of three collinear points?

What are the names of four coplanar points?

Naming Points, Lines, and Planes• TQ and line m.

• Plane RQV and plane RSV.

• Points R, Q, and S are collinear.• Points R, Q, S, and V are coplanar.

Defined Terms• Segment – a part of a line that consists of two

endpoints and all points between them.– Can name a segment by its two endpoints.

• Ray – a part of a line that consists of one endpoint and all the points of the line on one side of the endpoint.– Can name a ray by its endpoint and another point on

the ray.– The order of points indicates the ray’s direction.

• Opposite rays – two rays that share the same endpoint and form a line.– Can name opposite rays by their shared endpoint and

any other point on each ray.

Defined Terms

AB

AB

CA and CB

Name Segments and Rays• What are the names of the segments in the figure?• What are the names of the rays in the figure?• Which of the rays in the previous question are

opposite rays?

Name Segments and Rays• The three segments are DE or ED, EF or FE, and DF

or FD.

• The four rays are DE or DF, ED, EF, and FD or FE.

• The opposite rays are ED and EF.

Postulates

• A postulate or axiom is an accepted statement of fact.– Basic building blocks of the logical system in

geometry.– Use logical reasoning to prove general concepts.

Postulates• Postulate 1.1– Through any two points there is exactly one line.

• When you have two or more geometric figures, their intersection is the set of points the figures have in common.

• Postulate 1.2– If two distinct lines intersect, then they intersect in

exactly one POINT.

Postulates

• Postulate 1.3– If two distinct planes intersect, then they intersect

in exactly one LINE.

• Postulate 1.4– Through any three NONCOLLINEAR points, there is

exactly one plane.

More Practice!!!!!

• Classwork – Textbook p. 16 - 17 # 9 – 35 odd

• Homework – Textbook p. 16 - 17 # 8 – 36 even