# Math chapter 2: Properties, Postulates, Definitions, and Theorems

## 27 terms

### Addition POE

If a=b then a+c=b+c

### Subtraction POE

If a=b then a-c=b-c

### Multiplication POE

If a=b then c∗a=c∗b

### Division POE

If a=b and c≠0 then a÷c=b÷c

a=a

If a=b then b=a

### Transitive POE

If a=b and b=c then a=c

### Substitution POE

If a=b then b can be substituted for a

a(b+c)=ab+ac

∠A≅∠A

### Symmetric POC

If ∠A≅∠B then ∠B≅∠A

### Transitive POC

If ∠A≅∠B and ∠B≅∠C then ∠A≅∠C

### Linear Pair Theorem

If 2 angles form a linear pair then they are supplementary (NOTE: different from definition of linear pair which just states that a linear pair is a pair of adjacent angles whose non common sides are opposite rays)

### Congruent Supplements Theorem

If 2 angles are supplementary to the same angle or to two congruent angles, then the 2 angles are congruent. ex: if ∠1 and ∠2 are supplementary and ∠3 and ∠2 are supplementary, then ∠1≅∠3

### Right Angle Congruence Theorem

all right angles are congruent

### Congruent Complements Theorem

If 2 angles are complementary to the same angle or to two congruent angles, then the 2 angles are congruent. ex: if ∠1 and ∠2 are complementary and ∠3 and ∠2 are complementary, then ∠1≅∠3

### One Half Bisector Theorem

If →BX is the bisector of ∠ABC, then m∠ABX=1/2 m∠ABC and m∠XBC=1/2 m∠ABC

### Common Segments Theorem

If AB≅CD, then AC≅BD

### Common Angles Theorem

If ∠AXB≅∠CXD, then ∠AXC≅∠BXD

### Verticle Angle Theorem

If 2 angles are verticle angles, then they are congruent (NOTE: different from definition of verticle angles which just states that verticle angles are two non adjacent angles formed by two intersecting lines)

### Converse Statement

formed by exchanging hypothesis and conclusion

### Inverse Statement

formed by negating the hypothesis and conclusion

### Contrapositive Statement

formed by exchanging and negating the hypothesis and the conclusion

### Biconditional Statement

can be written in the form "p if and only if q." (both "if p then q" and "if q then p" are true)

### Angle Addition Postulate

m∠AXB+m∠BXC=m∠AXC

If a=b then a≅b

AB+BC=AC