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Geometry Sections 1.2 & 2.1 The Building Blocks of Geometry

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Geometry Sections 1.2 & 2.1 The Building Blocks of Geometry. Webster’s New World Dictionary, Third College Edition, gives the following definitions. turn: rotate: revolve:. t o rotate or revolve. to turn or cause to turn. t o turn.

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Presentation Transcript
slide2
Webster’s New World Dictionary, Third College Edition, gives the following definitions.turn: rotate:revolve:

to rotate or revolve

to turn or cause to turn

to turn

in our study of geometry in order to avoid circular definitions we will leave 3 terms undefined
In our study of geometry, in order to avoid circular definitions, we will leave 3 terms undefined.
point
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.

slide5
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 ( ).

plane
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 lie

in the same line ( )

slide7
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

slide10

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 axiomis

a statement that is accepted as true without proof.

slide11
Postulate 5: Through any two points there is exactly one line.What important idea about lines is indicated by this postulate?

lines must be straight

slide14
Postulate 8: Through any three noncollinear points there is exactly one line.What if the three points were collinear?

infinitely many planes contain

collinear points

slide16

Postulate 10: If two points lie in a plane then the line containing them is in the plane.What important idea about planes is indicated by this postulate?

planes must be flat

slide17

Postulate 1.1.5: If two planes intersect, then their intersection is a line.What important idea about planes is indicated by this postulate?

planes continue on without end

slide18

While it certainly may seem as though these postulates are not saying anything of any real importance, nothing could be farther from the truth. These postulates are in fact the basis of Euclidean geometry. For Euclid, planes are a flat surface like the floor and lines are straight like your pen or pencil. But what if we thought of a plane as being the surface of a sphere (i.e. the globe) and lines as being great circles on the sphere (i.e. the equator or any lines of longitude). Such thinking results in a whole different type of geometry called spherical geometry.

slide19

Example: Determine if the given set of points are collinear, coplanar, both or neither.1) B, D2) E, F, A3) B, C, D, E 4) E, F, G, A

slide20

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 ( ).

slide21

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 (________).

slide22
The intersection (symbol: ______) of two (or more) geometric figures is the set of points that are in both figures at the same time.
slide23
The union (symbol: ______) of two (or more) geometric figures is the set of points that are in one figure or the other or both.