Chapter 2 Proofs
Chapter 2 Postulates, Theorems, Formulas, and Converses
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- Multiplication/Division Property of Equality
- If a=b, then ac=bc (a/c=b/c) Cnot= 0
- Congruent Complements Theorem
- If two angles are complementary to the same angle then they are congruent to each other
- Reflexive Property of Equality
- For any real number, a, a=a
- Transitive Property of Equality
- If a=b and b=c then a=c
- Identity Property
- a+0=a and a*1=a
- Inverse Property
- a+(-a) = 0
- Postulate 6
- A line contains at least two points
- Congruent Supplements Theorem
- If two angles are supplementary or congruent to the same angle then they are congruent to each other
- Distributive Property of Equality
- If a(b+c), then ab+ac
- Right Angle Congruence Theorem
- All right angles are congruent
- Substitution Property of Equality
- If a=b then a/b can be substituted for b/a in any equation or expression
- Postulate 8
- Through any three noncollioner points there exists exactly one point
- Postulate 5
- Through any two points there exists exactly one line
- Linear Pair Postulate
- If two angles form a linear pair, then they are supplementary
- Postulate 9
- A plane contains at least three noncollionet points
- Postulate 7
- If two lines intersect, then their intersection is exactly one point
- Vertical Angle Theorem
- All vertical angles are congruent
- Addition/Subtraction Property of Equality
- If a=b, then a+c=b+c or a-c=b-c
- Symmetric property of Equality
- If a=b the b=a