A position in space with no size, weight, or volume. A point is represented by a dot and symbolized by a capital letter.
A straight set of points continuing indefinately in 2 directions. A line has no width, size or length. A line is represented by a double arrow with points and symbolized by naming two points or a single lower case letter as follows.
A flat surface extending indefinately in any direction. Planes have no thickness, size or weight. Planes are represented by parallelogram, and symbolized by one or more capital letters.
Points on the same line
Points on the same plane
A part of a line between and including 2 endpoints. A line segment is symbolized by naming its two endpoints and placing a bar on top. Segment names are reversible, so they can be moved two ways.
A part of a line beginning at a point called the endpoint and continuing forever in one direction. It is symbolized by two letters, the first which MUST be the endpoint and the other is any point on the ray. Rays can have many names. (first letter of ray= endpoint)
Two rays with a common endpoint going in opposite directions.
are segments that have the SAME LENGHT
of a segment is the point which divides the segment into two congruent parts
of a segment is any line, ray, segment, or plane that passes through the midpoint of the segment
is a way to represent lines, rays and segments while pairing points with numbers
Postulate 1: The Ruler Postulate
makes number lines
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC= AC
an angle whose measure is between 0 and 90%
and angle whose measure is exactly 90 degrees
an angle whose measure is between 90 and 180 degrees
and angle who measure is exactly 180 degrees
Are angles that have equal measures
are two angles in a plane that have a common vertex, common side, but no common interior points
Bisector of an ANGLE
is a line or ray that divides the angle into 2 congruent, adjacent angles
The Protractor Postulate
Postulate 4: Angle Addition Postulate
If point B lies in teh interior of angle AOC, then angle AOB + angle BOC= angle AOC
is a statement which can be accepted as true but can not be proven
A line contains at least two points.
A plane contains at least three noncollinear points.
Space contains at least four noncoplanar points
Through any two points there is exactly one line.
Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane
If two points are in a plane, then the line that contains those points is in that plane.
If two planes intersect, then their intersection is a line.
statement that can be proven
If two lines intersect, then they intersect at exactly one point
Through a line and a point NOT in the line there is exactly one plane
If two lines intersect, then exactly one plane contains the lines
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