# Geometry Honors #3

## 32 terms

### parallel lines

lines in the same plane that never intersect

### skew lines

noncoplanar lines that never intersect

### parallel postulate

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

### transversal

a line that intersects two coplanar lines at two distinct points

### corresponding angles postulate

If a transversal intersects two parallel lines, then the corresponding angles are congruent.

### alternate interior angles theorem

If a transversal intersects two parallel lines, then the alternate interior angles are congruent

### same side interior angles theorem

If a transversal intersects two parallel lines, then the same-side interior angles are supplementary.

### alternate exterior angles theorem

If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.

### converse of corresponding angles postulate

If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

### converse of alternate interior angles theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

### converse of same side interior angles theorem

If two lines and a transversal form same side interior angles that are supplementary, then the two lines are parallel.

### converse of alternate exterior angles theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

### parallel lines theorem

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

### slope formula

rise/run, (Y2-Y1)/(X2-X1)

### slopes of lines theorem (1)

In a coordinate plane, two distinct nonvertical lines are parallel iff they have the same slope.

### slopes of lines theorem (2)

In a coordinate plane, two nonvertical lines are perpendicular iff their slopes are negative reciprocals of each other. (product of their slopes = -1)

y = mx + b

### standard form

Ax + By = C, where A and B are not both zero

### perpendicular lines theorem (1)

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

### perpendicular lines theorem (2)

Two lines are perpendicular iff they intersect to form four right angles.

### perpendicular transversal theorem

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

### 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.

### distance from a point to a line

length of the perpendicular segment from the point to the line

### perpendicular lines

lines that intersect to form right angles

### theorem

statement that can be proven

### midpoint theorem

If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB.

### angle bisector theorem

If ray BX is the bisector of angle ABC, then the measure of angle ABX= 1/2 m<ABC and m<XBC= 1/2 m<ABC (< = angle).

### congruent supplements theorem

If two angles are supplementary to the same angle (or congruent angles), then the two angles are congruent.

### congruent complements theorem

If two angles are complementary to the same angle (or congruent angles), then the two angles are congruent.

### linear pair postulate

Linear pairs are supplementary.

### vertical angles theorem

Vertical angles are congruent