absolute value
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between
B is between A and C if 1) A B and C are different points on the same line, and 2) AB + BC = AC
line postulate
for every two points there is exactly one line that contains both points
segment
for any points A & B the segment AB is the union of A & B and all points that are between A & B
ray
the ray AB is the union of AB and the set of all points C for which A-B-C
opposite rays
if B-A-C then AB and BC are called opposite rays
midpoint
a point B is called the midpoint of a segment AC if B is between A and C and AB=BC
PPT
let Ab be a ray & let X be a positive number. There is exactly one point P on AB such that AP= x
ACP
let AB be a ray on the edge of the half-plane H. For every number r between 0 and 180 there is exactly one ray AP, with P in H, such that m<PAB= r
AAP
if D is in the interior of <BAC, then m<BAC= m<BAD + m<DAC
linear pair
if AB and AD are opposite rays and AC is any other ray, then <BAC and <CAD form a linear pair
supplement postulate
if two angles form a linear pair, then they are supplementary
supplement theorem
supplements of congruent angles are congruent
vertical angles
two angles are vertical angles if their sides form two pairs of opposite rays
VAT
vertical angles are congruent
ITT
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
CIT
if two angles of a triangle are congruent, then the sides opposite those angles are congruent
median
a median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
corollary 6-2.1
given a segment AB and a line L in the same plane. If two points of L are each equidistant from A and B, then L is the perpendicular bisector of AB
PBT
the perpendicular bisector of a segment, in a plane, is the set of all points of the plane that are equidistant from the endpoints of the segment
perpendicular bisector
in a given plane, the perpendicular bisector of a segment is the line which is perpendicular to the segment at its midpoint
EAT
an exterior angle of a triangle is greater than each of its remote interior angles
line perpendicular to a plane
a line and a plane are perpendicular if they intersect and if every line lying in the plane and passing through the point of intersection is perpendicular to the given line
BTP
If a line is perpendicular to each of two intersecting lines at their point of intersection, then it is perpendicular to the plane that contains them
perpendicular bisecting plane theorem
The perpendicular bisecting plane of a segment is the set of all points equidistant from the endpoints of the segment