Chapter 3 Theorems/Definitions/Postulates

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Slope for two points

m= y2-y1/x2-x1

Slope-Intercept Equation

y= mx+b

Point-Slope Equation

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

Negative Slope

falls left to right

Positive Slope

rises left to right

Zero Slope

horizontal

Undefined Slope

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

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

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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

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