through any two points there is exactly one line
If two lines intersect, they intersect in exactly one point
if two planes intersect then they intersect in exactly one line
through any three collinear points there is exactly one plane
postulate 1-5 (ruler postulate)
points of a line can be put into one to one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers
postulate 1-6 (segment addition)
if three points A, B,and C are collinear and B is between A and C, then AB+BC=AC.
postulate 1-7 (protractor postulate)
ray OA, OB, and all other rays with endpoint O can be drawn on one side of line AB can be paired with the real numbers from 0 to 180 so that if ray OC is paired with x and ray OD is paired with y, then m<COD= absolute value of x-y.
postulate 1-8 (angle addition)
if point B is in the interior of <AOC, then m<AOB+m<BOC=m<AOC. If <AOC is a straight angle, then m<AOB+m<BOC=180.
If two figures are congruent then their two areas are equal.
The area of a region is the sum of the areas of its nonoverlapping parts.