Unit 1 Flashcards
Point
Location, like a dot on a map or computer
Line
Infinite set of points, the idea of straightness
Plane
Infinite set of points, idea of flatness extending in all directions
Space
set of all points
Collinear points
points that all lie on the same line
Coplanar points
points that all lie on the same plane
Intersection
of 2 figures, it is the set of points that both figures have in common
Line segment/ segment LINE AB
LINE AB consists of the endpoints of A & B and all points on LINE AB that are between A & B
RAY AB
initial point A and all points on RAY AB that lie on the same side of A as point B
Opposite Rays
Start on same point, goes in different directions
————————————>
A B
Ray, RAY AB
<—————–————-————*—————->
A C B
Opposite ray= RAY CA and RAY CB
Postulate
Statement that’s accepted as truth without proof
Postulate #1
Ruler Postulate - Points in a line can be matched with 1:1 real numbers. The real number corresponds to a point is the coordinate of the point
The distance between points A & B is written as LINE AB. It is calculated as the absolute value of the difference between the coordinates of A & B. This is called the length of LINE AB
EX:
5 Units
—————————-
<–|—-|—-|—-|—-|—-|—-|—-|—>
1 2 3 4 5 6 7 8
|2-7|=5, this means the line’s length is 5 units long.
Length of the line?
*---------------------------------* <--|----|----|----|----|----|----|----|---> -1 0 1 2 3 4 5 6
|-1-5|= 6
6 units
Postulate #2
Segment Addition Postulate - If B is between A & C, then AB + BC = AC, if Ab + BC = AC, then B is between A & C
Congruent segments
Segments that have the same lengths, symbol ≌
Midpoint of a segment
The point that divides the segment into 2 congruent segments
Bisector of a segment
a line, segment, ray, or plane that intersects the segment at its midpoint
Angle
Consists of 2 different rays that have the same initial point
Sides of the angle
Rays
Vertex of the angle
initial point
Measure of an angle
m<a
Congruent angles
angles that are equal in measure
Between
a point that is on a line between two other lines
EX:
Point B IS between points A & C
<——————-—————–*———>
A B C
Point B IS NOT between points A & C
<————————————-———>
A C
*
B
Postulate #4
Angle Addition Postulate
If point B lies in the interior of ∠AOC then
m∠AOB + m∠BOC = m∠AOC
Linear pair postulate
If ∠AOC is a straight angle and B is any point not on AC, then
m∠AOB + m∠BOC = 180
Adjacent Angles
Two angles are adjacent if they share a common vertex and side, but no common interior points
Postulate #5
-A line contains at least two points
-A plane contains at least three points not all in one line
-Space contains at least four points not all in one place
Postulate #6
Through any two points there is exactly one line
Postulate #7
Trough any three points there is at least one (infinite) plane, nd through any three noncollinear points there is exactly one plane (only one).
Postulate #8
If two points are in a plane, then the line that contains the points is in that plane
Postulate #9
If two planes intersect, then their intersection is a line
Theorems
Important statements in geometry that are proved
Theorem #1
If two lines intersect, then they intersect in 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
TRUE OR FALSE: Two points can lie in each of two different lines
False
TRUE OR FALSE: Three noncollinear points can lie in each of two different planes
False
TRUE OR FALSE: Three collinear points lie in only one plane
False
TRUE OR FALSE: Two intersecting lines are contained in exactly one plane
True
If two lines intersect, then they intersect in exactly one point
True
If two planes intersect, then their intersection is a line
True
