# Ch. 3 Geometry- Lines, Angles

### 36 terms by kmazzarella

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### parallel lines

do not intersect, coplanar

### skew lines

do not intersect, not coplanar

do not intersect

### 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.

### transversal

a line that intersects two or more coplanar lines at different points

### corresponding angles

2 angles in corresponding positions relative to the 2 lines (w/ transversal)

### alternate interior angles

2 angles between 2 lines and on opposite sides of a transversal

### alternate exterior angles

2 angles that lie outside 2 lines and on opposite sides of a transversal

### 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.

### paragraph proof

statements and reasons written in sentences

### slope

ratio of vertical change (rise) to horizontal change (run) between any two points on the line

### slope equation

m= rise/run = change in y / change in x = (y2-y1) / (x2-x1)

### negative slope

falls from left to right

### positive slope

rises from left to right

horizontal

vertical

### 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.

### slope-intercept form

y = mx + b
m is the slope; b is the y-intercept

### standard form

Ax +By = C when A & B are not both zero

### 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.

### distance from a point to a line

the length of the perpendicular segment from the point to the line (shortest distance)

Example: