Ch. 1-2 postulates and theorems
the points on a line can be paired with all real numbers and the distance on the line is found by taking the absolute value of the difference of their coordinates.
Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.
Given a strait angle rays can be paired with numbers from 0 to 180. the measure of an angle is the absolute value of the difference of the numbers paired with rays.
Angle Addition Postulate
If P is in the interior of RST, then mRST=mRSP+mPST
A line contains at least 2 points, a plane at least 3 non collinear points, and space at least 4 non coplanar points.
Through any two points there exists exactly one line.
7, Any 3 points are contained in at least one plane, and 3 non-collinear points determine a plane.
flat plane postulate
if two points lie in a plane, then the line containing those points lies in the plane
plane intersection postulate
9, if two planes intersect, then their intersection is a line
, if a=b and c=d, then a+c=b+d
If a=b and c=d, then a-c=b-d
If a=b, then ac=bc
if a=b and c≠0, then a/c=b/c
if a = b, then a can be substituted for b in any equation or expression
If a=b, then b=a
If a=b and b=c, then a=c
line intersection theorem
2 different lines intersect in at most ONE POINT
plane determination theorem
Through a line and a point not on a line, there is exactly one plane.
if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB
Angle Bisector theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
If two angles for a linear pair, then they are supplementary angles
verticle angle theorem
If two angles are vetical angles, then they have equal measures
perpendicular lines form congruent adjacent angles.
if 2 lines for congruent adjacent angles then they are perpendicular.
if the outside rays of two adjacent acute angles are perpendiculalr, then the angles are complementary.
supplements of congruent angles theorem
supplements of congruent angles are congruent
compliments of congruent angles theorem
compliments of congruent angles are congruent