The following is a list of some of the postulates and theorems presented so far this year. You
may want to go back in your books to add any missing definitions, postulates, or theorems that
you need to study.
A segment has a length, and you could find the length by putting it in a
number line or using a ruler. The points on a line can be matched one to one with the real
numbers. The real number that corresponds to a point is the coordinate of the point.
ment Addition Postulate:
If B is between A and C, then AB+AC=AC. If
AB+BC=AC, then B is between A and C.
The rays in an angle can be matched one to one with the real
numbers from 0 degrees to 180 degrees. The measure of angle AOB is e
qual to the
absolute value of the difference between the real numbers for ray OA and ray OB.
Angle Addition Postulate:
If P is the interior of angle RST, then the measures of angle
RST is equal to the sum of the measures of angle RSP and angle PST. The mea
angle RST = RSP + PST
DON’T NAME BY POSTULATE 5!
Through any two points there exists exactly one line.
A line contains at least two points.
If two lines intersect, then their intersection is exactly one point.
Through any three noncollinear points there exists exactly one plane
(example is a wobbling chair will always have three legs on the ground at once).
A plane contains at least three noncollinear points.
If two point
s lie in a plane, then the line containing them lies
on that plane.
If two planes intersect, then their intersection is a line.
Right Angle Congruence Theorem (RAT):
All right angles are congruent. Because all
right angles equal 90 degrees.
Congruent Supplement Theorem (CST):
If two angles are supplements of the same
angle, then they are congruent.
Congruent Complement Theorem (CCT):
If two angles are complements of the same
angle then they are congruent.
Linear Pair Postulate:
If two angles
form a linear pair then they are supplementary.
Vertical Angle Congruence Theorem (VAT):
Verticals angles are congruent.