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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.
to rotate or revolve
to turn or cause to turn
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.
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 ( ).
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 ( )
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.
lines must be straight
infinitely many planes contain
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
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
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.
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
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 ( ).
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 (________).