Postulate 1: Ruler Postulate
points on a line can be matched with real numbers.
Postulate 2: Segment Addition Postulate
if b is between a and c, then ab + bc = ac.
Postulate 3: Protractor Postulate
the measure of any angle is equal to the absolute value of the difference between the real numbers for oa and ob.
Postulate 4: Angle Addition Postulate
if P is in the interior of RST, then the measurement of RST is equal to the sum of the measures of RSP and PST.
Postulate 5: Two Points Postulate
Through any two points there is exactly one line.
Postulate 6: How many points in a line?
A line contains at least two points
Postulate 7: Intersecting Lines
If two lines intersect, then their intersection is exactly one point.
Postulate 8: 3 noncollinear Points
Through any three noncollinear points there exists exactly one plane
Postulate 9: Intersecting Planes
If two planes intersect, then their intersection is a line
Postulate 10: 2 points lie in a plane - what about the line containing them?
If two points lie in a plane, then the line containing them lies in the same plane
Postulate 11: Intersecting Planes
If 2 planes intersect, then their intersection is a line.
Theorem 2.1: Segment Congruence
Reflexive, Symmetric, Transitive
If AB = CD, then CD = AB.
If AB = CD and CD = EF, then AB = EF.
Theorem 2.3: Right Angles
All right angles are congruent.
Theorem 2.4: Supplementary Angles - congruent?
If 2 angles are supplementary to the same angle (or to congruent angles) then they are congruent.
Theorem 2.5: Complementary Angles - congruent?
If 2 angles are complementary to the same angle (or to congruent angles) then they are congruent.
Postulate 12: Linear Pairs
If two angles form a linear pair, then they are supplementary.
Theorem 2.6: Vertical Angles
Vertical angles are congruent.
Postulate 13: Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
Postulate 14: Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Postulate 15: Corresponding angles
corresponding angles are congruent
Theorem 3.1: Alternate angles
alternate interior and exterior angles are congruent
Theorem 3.3: Consecutive Interior Angles
consecutive interior angles are supplementary
Postulate 16: Corresponding Angles Converse
if 2 lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Theorem 3.4: Alternate Interior/Exterior angles converse
If the alternate interior and exterior angles are congruent, the lines are parallel.
Theorem 3.6: Consecutive Interior Angles Converse
If the consecutive interior angles are supplementary, the lines are parallel.
Please allow access to your computer’s microphone to use Voice Recording.
We can’t access your microphone!
Click the icon above to update your browser permissions above and try again
Reload the page to try again!
Press Cmd-0 to reset your zoom
Press Ctrl-0 to reset your zoom
It looks like your browser might be zoomed in or out. Your browser needs to be zoomed to a normal size to record audio.
Your microphone is muted
For help fixing this issue, see this FAQ.