# Chapter 3 - Postulates and Theorems

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### Unique Measure Assumption

every angle has a unique measure from 0 degrees to 180 degrees

### Unique Angle Assumption

given a ray and any real number between 0 and 180 there is one unique angle

### Straight Angle Assumption

if ray BA and ray BC are opposite rays then m<ABC = 180 degrees

### Zero Angle Assumption

if ray XY and ray XZ are the same ray then m<XYZ = 0 degrees

If angles AVC and CVB are adjacent angles, then m<AVC + m<CVB = m<AVB

### Corresponding Angles Postulate

a. If 2 corresponding angles have the same measure, then the lines are parallel
b. If 2 lines are parallel, then the corresponding angles have the same measure

### Linear Pair Theorem

if 2 angles form a linear pair, then they are supplementary

### Vertical Pair Theorem

if 2 angles are vertical angles, then they have equal measures

### Parallel Lines and Slopes Theorem

2 non-vertical lines are parallel if and only if they have the same slope

### Perpendicular Lines and Slopes Theorem

2 non-vertical lines are perpendicular if and only if the product of their slopes is -1

a = a

### Symmetric Property

if a = b, then b = a

### Transitive Property

if a = b and b = c, then a = c

a = b, then a + c = b + c

### Subtraction Property of Equality

a = b, then a - c = b - c

### Multiplication Property

if a = b, then a x c = b x c

### Division Property of Equality

if a = b, then a/c = b/c

### Transitive Property of Inequality

if a < b and b < c, then a < c

a < b, then a + c < b + c

### Multiplication Property of Inequality

if a < b, then a x c < b x c (if c > 0)
if a < b, then a x c > b x c (if c < 0)

### Substitution Property of Equality and Inequality

if a = b, then a may be substituted for b

Example: