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### parallel postulate

If there is a line and a point not on the line, then there is exactly one line through the point 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 perpendicular to the given line.

### consecutive interior angles (same-side interior angles)

2 angles between 2 lines and on the same side of a transversal

### corresponding angles postulate

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

### alternate interior angles theorem

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

### alternate exterior angles theorem

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

### consecutive interior angles theorem

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

### 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.

### transitive property of parallel lines

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

### slopes of parallel lines postulate

In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope.

### slopes of perpendicular lines postulate

In a coordinate plane, two non-vertical lines are perpendicular if and only if the products of their slopes equals -1 (slopes of perpendicular lines are negative reciprocals). Horizontal lines are perpendicular to vertical lines.

### linear pair perpendicular lines theorem

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

### four right angles theorem

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

### complementary adjacent acute angles theorem

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.