Chapter 1 Flashcards
space
set of all points
collinear points
points all in one line
coplanar points
points all in one plane
ruler postulate
- 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
- 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
segment addition postulate
if B is between A and C, then AB+BC=AC
congruent
two objects that have the same size and shape
congruent segments
segments that have equal lengths
midpoint of a segment
the point that divides the segment into two congruent segments
bisector of a segment
a line, segment, ray, or plane that intersects the segment at its midpoint
angle
the figure formed by two rays that have the same endpoint
sides
two rays of the angle
vertex
common endpoint of two rays
acute angle
measures between 0 and 90
right angle
measures 90
obtuse angle
measures between 90 and 180
straight angle
measures 180
protractor postulate
rays of an angle can be paired with the real numbers from 0 to 180
angle addition postulate
- if point B lies in the interior of angle AOC, then angle AOB plus angle BOC = AOC
- if angle AOC is a straight angle and B is any point not on line AC, then AOB+BOC=180
congruent angles
angles that have equal measures
adjacent angles
two angles in a plane that have a common vertex and a common side but no common interior points
bisector of an angle
the ray that divides the angle into two congruent adjacent angles
postulate about number of points
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 plane
postulate about points on a line
through any two points there is exactly one line
postulate about three points and a plane
through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane
postulate about two points and a plane
if two points are in a plane, then the line that contains the points is in that plane
postulate about planes intersecting
if two planes intersect, then their intersection is a line
theorem 1-1
if two lines intersect, then they intersect in exactly one point
theorem 1-2
through a line and a point not in the line there is exactly one plane
theorem 1-3
if two lines intersect, then exactly one plane contains the lines
