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Geometry; Chapter 1
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Terms in this set (40)
Point
The simplest and yet most important building block in geometry. It is a location and occupies no space, height, length or width. We can't actually draw one.
(Single uppercase letter)
Line/Straight Line
Infinite series of points. Extends infinitely in two opposite directions, but has no width and no height.
(named as 2 points or a single lowercase letter)
Ray
Part of a line consisting of a given point, called the endpoint, and the set of all points on one side of the end point.
(named as 2 points)
Opposite Rays
Rays that have the same end point and that form a line
Angle
The union of two rays having the same endpoint. The end point is called the vertex, and the rays are called the sides
(named by letter, 3 letters, or #)
Plane
Infinite set of points extending in all directions along a perfectly flat surface. It is infinitely long and infinitely wide. A thickness (a height) of 0
(single uppercase letter often represented as a four sided figure)
Coplanar Points
Points in the same (only one) plane
Collinear Points
Points on the same line
Line Segment
A part of a line consisting of 2 points, called end points, and the set of all points in between them.
(named as 2 points)
Segment Addition Postulate
If B is between A and C, the AB + BC = AC
Length
Looks like a line without endpoints of arrows. It is asking for a number/measurement
(named by 2 points)
Ruler Postulate
1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1
2. Once a coordinate system has been chosen in this way, the distance between any two points equals in absolute value of the difference of their coordinates.
Angle Addition Postulate
If B lies in the interior of Angle AOC, the measure of angle of AOB + measure of angle BOC = measure of angle AOC
Congruent
same size and shape
Congruent Segments
segments have equal lengths
Midpoint of a Segment
is a point that divides the segment into two congruent segments
Bisector of a Segment
is a line, segment, ray, or plane that intersects the segment at its midpoint.
Congruent Angles
angles that have equal measures
Adjacent Angles
are two angles in a plane that have a common vertex and a common side but no common interior points
Bisector of an Angle
is the ray that divides the angle into two congruent adjacent angles
Postulates
a basic assumption accepted with proof
Theorem
a statement that can be proved using postulates, definitions, and previously proved theorems
Exists
there is at least one
Unique
there in no more than one
One and Only One
exactly one
Determine
to define or specify
The Protractor Postulate
gives us the values of the angles (180)
1. a line contains at least ____ points
2.a plane contains at least ____ points that aren't _____
3. space contains are least ____ points that aren't _____
1. two
2. three, noncollinear
3. four, noncollinear
Through and two points there is....
exactly one line
Through any three points there is...
Through any three noncollinear points there is....
at least one plane
exactly one plane
if two points are in a plane, the the line that contains the points is...
in that plane
If two plane interest, then their intersection is.....
a line
If two lines intersect, then they intersect in....
exactly one point
Through a line and a point (not in that line) there is...
exactly one plane
If two lines intersect, then exactly one plane...
contains the lines
Relationship between points
1. two points must be...
2. three points may be...
3. three noncollinear points must be...
4. Four points may be...
5. Four noncoplanar points determine a....
1. collinear
2. collinear or noncollinear
3. coplanar
4. coplanar or noncoplanar
5. a plane
Determine a plane
1. three noncollinear points
2. a line and point (not on that line)
3. two intersecting lines
Relationship between two lines in the same plane
either parallel or intersect in one point
Relationship between a line and plane
1. parallel
2. intersect in one point
3. plane contains the line
Relationship between two planes
parallel or intersection is a line
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