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# Reasoning and Proof

### general postulates and theorems (Chp. 2)

hypothesis conclusion
Through any two points there is exactly one line
Through any three points not on the same line there is exactly one plane
A line contains at least two points
A plane contains at least three points not on the same line
If two points lie in a plane then the entire line containing those points lies in that plane
If two lines intersect then their intersection is exactly one point
If two planes intersect then their intersection is a line
If M is the midpoint of line AB then line AM is congruent to line MB
The points on any line or line segment can be paired with real numbers so that given any two points A and B on a line, A corresponds to zero, and B corresponds to a positive real number
If B is between A and C then AB+ BC= AC
Congruence of segments is reflexive, symmetric, and transitive
Given the ray AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of ray AB, such that the measure of the angle formed is r
If R is in the interior of angle PQS, then the measure of angle PQR plus the measure of angle RQS equals the measure of angle PQS. If the measure of angle PQR plus the measure of angle RQS will equal the measure of angle PQS, then R is the interior of angle PQS
If two angles form a linear pair, then they are supplementary angles
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles
Congruence of angles is reflexive, symmetric, and transitive
Angles supplementary to the same angle or to congruent angles are congruent
Angles complementary to the same angle or to congruent angles are congruent
If two angles are verticle angles, then they are congruent
Perpendicular lines intersect to form four right angles
All right angles are congruent
Perpendicular lines form congruent adjacent angles
If two angles are congruent and supplementary, then each angle is a right angle
If two congruent angles form a linear pair, then they are right angles
Conclusion In a conditional statement, the statement that immediately follows the word "then".
Converse The statement formed by exchanging the hypothesis and conclusion of a conditional statement.
Hypothesis In a conditional statement, the statement that immediately follows the word "if".
Inverse The statement formed by negating both the hypothesis and conclusion of a conditional statement.
Created by: m.meyer