Geometry: chapter 1 Flashcards
ray
all points on a line on one side of an endpoint
segment of a line
two points of a line and all the points between them
opposite rays
the set of points on a line on opposite side of an endpoint
length of a line segment
distance between the endpoints
postulate
a statement we accept as true without proof
postulate 1: ruler postulate
the points on a line can be paired with real numbers in such a way that any two points can have coordinates 0 and 1
once a coordinate system has been chosen in this way the distance between any two points equals the absolute value of the difference of their coordinates
postulate 2: ruler postulate
If B is between A and C then AB+BC=AC
congruent
two objects that have the same size and same shape
congruent segments aer segments that have the same length
midpoint of a segment
the pointts that divides a segment into two congruent segments
bisector of a segment
a line segment, ray or plane at intersects the segment at its midpoint
space
set of all points
plane
intuitive idea
colinear points
points all in one line
coplanar points
points all in one plane
intersection of two figures
set of points that are in both figures
angle
figure formed by two rays that have the same endpoint
sides of the angle
two rays that form the angle
vertex
common endpoint of the angle
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
through any three points there is at least one plane and through any three noncollinear points there is exactly one plane
postulate 8
If two points are in a plane than the line that contains the points are in that plane
postulate 9
if two planes intersect then their intersection is a line
theorems
important statements that are proved
theorem 1-1
If two lines intersect then there intersect is exactly one point
theorem 1-2
Through a line and a point not in that line there is exactly one plane
theorem 1-3
If two lines intersect then exactly one plane contains the line
