# Chapter 3 Theorems/Definitions/Postulates

### 19 terms by 14griann

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m= y2-y1/x2-x1

y= mx+b

(y-y1)= m(x-x1)

### Negative Slope

falls left to right

### Positive Slope

rises left to right

horizontal

Vertical

### Transitive Property of Parallel Lines

If two lines are parallel to the same line, then they are parallel to each other

### Corresponding Angles Converse

If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel

### Alternate Interior Angles Converse

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel

### Alternate Exterior Angles Converse

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel

### Consecutive Interior Angles Converse

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel

### Slopes of Parallel lines

two nonvertical lines are parallel if and only if they have the same slope; any two vertical lines are parallel

### Slopes of perpendicular lines

two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines.

### ...

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

### ...

If two lines are perpendicular, then they intersect to form four right angles

### ...

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

### Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

### Lines Perpendicular to a Transversal Theorem

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Example: