geometry sections 1.2 & 2.1 the building blocks of geometry

Geometry Sections 1.2 & 2.1The Building Blocks of Geometry

In our study of geometry, in order to avoid circular definitions, we will

leave 3 terms undefined.

point: Usually described as a dot but actually has no size. Named by a capital letter.

Note: When you see a capital letter in a figure, it represents a point even if the point is not drawn.

line: A set of points that continues on without end in two opposite directions. Named by a single lower case letter ( )or any two points on the line ( ).

mor m lineBAor AB

plane:

A set of points that extends without end in 2 dimensions. Named by a single capital letter placed in a corner ( )or by 3 points that do not all liein the same line ( )

Mor M plane

BCA plane

Points are collinear if they lie on the same line.

In the description of a plane, we talked about 3 points not on the

same line. Three points not on the same line are called ___________.noncollinear

1) Draw an example of four collinear points

2) Draw an example of four noncollinear points

Points are coplanar if they lie on the same plane.

Points are noncoplanar if they do NOT lie on the same plane.

1)Draw an example of four coplanar points.

2) Draw an example of four noncoplanar points.

Example: Determine if the given set of points are collinear, coplanar, both or neither.1) B, D

2) E, F, A

3) B, C, D, E

4) E, F, G, A

both

coplanar

neither

neither

Just as undefined terms are the starting point for the vocabulary of geometry, postulates are going to be the starting point for the rules of geometry. A postulate or axiom is

a statement that is accepted as true without proof.

Postulate 5: Through any two points there is exactly one line.

lines must be straight

Postulate 8: Through any three noncollinear points there is exactly

one Plane.

Postulate 9: A plane contains at least 3 noncollinear points.

Postulate 10: If two points lie in a plane then the line containing

them is in the plane.

Postulate 11: If two planes intersect, then their intersection is

a line.

A line segment or segment is part of a line that begins at one point and ends at a second. Segments are named by

their two endpoints ( ).

BAor AB

A ray is a part of a line that begins at one point and extends infinitely in one direction. Rays are named

by their endpoint and another point on the ray (________).BCor BA

The intersection (symbol: ______) of two (or more) geometric figures is the set of points that are in both

figures at the same time.

**set of points that they SHARE**

Examples

A B C

1. Ray AC ray CA

2. Ray BD ray CA

3. Segment AB segment BC

D

The union (symbol: ______) of two (or more) geometric figures is the set of points that are in one figure

or the other or both.

Examples

DA B C

1. Line AB ray BC

2. Line segment AB line segment BC

3. Ray BD ray CA

Example: Determine the following intersections and unions based on the figure below.

DI

FH

DI

Example: Determine the following intersections and unions based on the figure below.

F

GE