- A postulate is a statement that is assumed true without proof.
- A theorem is a true statement that can be proven.
postulate
Let a , b and c be real numbers.
- Reflexive Property - a=a (A quantity is congruent (equal) to itself.)
- Symmetric Property - If a=b, then b=a
- Transitive Property - If a=b and b=c , then a=c
- Addition Postulate - If a=b , then a+c=b+c
- Subtraction Postulate - If a=b , then a−c=b−c
- Multiplication Postulate - If a=b , then ac=bc
- Division Postulate - If a=b and c≠0 , then ac=bc
- Substitution Postulate - If a=b , then a can be substituted for b in any expression.
- Distributive Postulate - a(b+c)=ab+ac
- A straight line contains at least two points.
- If two lines intersect, the intersection is only one point.
- If two planes intersect, the intersection is only one line.
- A plane must contain at least three noncollinear points.
theorem
- Congruence of Segments
- Segment congruence is reflexive, symmetric, and transitive.
- Reflexive - For any segment AB, ABAB is congruent to AB
- Symmetric - If AB=CD , then CD=AB
- Transitive - If AB=CD and CD=EF . then AB=EF
- Congruent Angles
- Angle congruence is reflexive, symmetric, and transitive.
- Reflexive - For any ∠A, ∠A=∠A
- Symmetric - If ∠A=∠B , then ∠B=∠A
- Transitive - If ∠A=∠B and ∠B=∠C, then ∠A=∠C
- Right Angle Congruence
- All right angles are congruent.
- Congruent Supplements
- If two angles are supplementary to the same angle, then they are congruent.
- If two angles are supplementary to congruent angles, then they are congruent.
- Congruent Complementary
- If two angles are complementary to the same angle, then they are congruent.
- If two angles are complementary to congruent angles, then they are congruent.
- Vertical Angles Congruence
- Vertical angles are always congruent.
