34 terms

# Chapter 1: Points, Lines, Planes and Angles

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Point
A position in space with no size, weight, or volume. A point is represented by a dot and symbolized by a capital letter.
Line
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.
Plane
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.
Space
set of all points
Collinear Points
Points on the same line
Coplanar
Points on the same plane
Segment
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.
Ray
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)
Opposite Rays
Two rays with a common endpoint going in opposite directions.
Congruent segments
are segments that have the SAME LENGHT
Midpoint
of a segment is the point which divides the segment into two congruent parts
Bisector
of a segment is any line, ray, segment, or plane that passes through the midpoint of the segment
Number Line
is a way to represent lines, rays and segments while pairing points with numbers
Postulate 1: The Ruler Postulate
makes number lines
If B is between A and C, then AB + BC= AC
Acute Angle
an angle whose measure is between 0 and 90%
Right Angle
and angle whose measure is exactly 90 degrees
Obtuse Angle
an angle whose measure is between 90 and 180 degrees
Straight Angle
and angle who measure is exactly 180 degrees
Congurent Angles
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
Postulate 3
The Protractor Postulate
If point B lies in teh interior of angle AOC, then angle AOB + angle BOC= angle AOC
Postulate
is a statement which can be accepted as true but can not be proven
Postulate 5
A line contains at least two points.
A plane contains at least three noncollinear points.
Space contains at least four noncoplanar points
Postulate 6
Through any two points there is exactly one line.
Postulate 7
Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane
Postulate 8
If two points are in a plane, then the line that contains those points is in that plane.
Postulate 9
If two planes intersect, then their intersection is a line.
Theorem
statement that can be proven
Theorem 1
If two lines intersect, then they intersect at exactly one point
Theorem 2
Through a line and a point NOT in the line there is exactly one plane
Theorem 3
If two lines intersect, then exactly one plane contains the lines