Math Chapter 3

Definition of Parallel Lines

Two lines that do not intersect and are coplanar.

Definition of Skew Lines

Two lines that do not intersect and are not coplanar.

Definition of Parallel Planes*

A plane is parallel to a line or plane if it does not intersect with it.

Parallel Postulate

If there is a line and a point not on the line, then there is EXACTLY ONE line through the point that is parallel to the given line.

Perpendicular Postulate

If there is a line and a point not on the line, then there is EXACTLY ONE line through the point that is perpendicular to the given line.

Definition of Transversal Line

A line that intersects TWO or more COPLANAR lines at DIFFERENT points.

Definition of Corresponding Angles (lock)

Two angles in Corresponding positions RELATIVE to the two lines.

Definition of Alternate Interior Angles

Angles that lie BETWEEN the two lines and on opposite sides of the transversal.

Definition of Alternate Exterior Angles

Angles that lie outside the two lines and on the opposite sides of the transversal.

Definition of Consecutive Interior Angles

Angles that lie BETWEEN the two lines and on the same side of the transversal.

How to find unobvious angles?

1. Check Linear Pairs

2. Double check for transitives + parallels

3. Look for corresponding

4. Look for zigzags (alternates)

Only ONE parallel pair

Only use the straight down safe angles from one non parallel line

Perpendicular Transversal Theorem

In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

Converse Perpendicular Transversal Theorem

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

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Consecutive Interior Angles Theorem

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

Angles Theorem

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

When to use PT theorem and Converse PT theorem?

To find perpendicular lines / To find parallel lines

Transitive Property of Parallel Lines

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

Converse Corresponding Angles Postulate

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

Converse Alternate Interior Angles Theorem

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

Converse Consecutive Interior Angles Theorem

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

Converse Alternate Exterior Angles Theorem

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