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36 terms

Ch. 3 Geometry- Lines, Angles

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parallel lines
do not intersect, coplanar
skew lines
do not intersect, not coplanar
parallel planes
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
zero slope
horizontal
undefined slope
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)