postulates, converses, laws, and theorms

Law of Detachment

If the hypothesis of a true conditional statement is true, then the conclusion is also true

Law of Syllogism

If hypothesis p, then conclusion q.

If hypothesis q, then conclusion r.

If hypothesis p, then conclusion r.

P = Q, Q = R, therefore P = R

Two Point Postulate

Through any two points, exactly one line exists.

Line Point Postulate

A line contains at least two points

Line Intersection Postulate

If two lines intersect, then their intersection is exactly one point

Plane Intersection Postulate

If two planes intersect, then their intersection is a line

Three-Point Postulate

Through any three noncollinear points exists exactly one plane

Plane-Point Postulate

A plane contains at least three noncollinear points

Right Angle Congruence Theorem

All right angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same angle, then they’re congruent

Congruent Complements Theorem

If two angles are complementary to the same angle, then they’re congruent

Linear Pair Postulate

If two angles form a linear pair, then they’re supplementary

Vertical angles Congruence Theorem

Vertical angles are congruent