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32 terms

Geometry 3.1-3.6

I hate this class... too many postulates!
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Two Parallel lines
Do not intersect and are coplanar
Two skew lines
do not intersect and are not coplanar
Transversal
line that intersects two or more coplanar lines at different points
Corresponding Angles
Corresponding positions and congruent
Alternate interior angles
They lie between 2 lines and on opposite sides and Congruent
Alternate Exterior
They lie outside the 2 lines and are on opposite sides and congruent
Consecutive interior
They lie between two lines and on the same side and supplementary
Transitive Property of Parallel Lines
if p≅q & q≅r, then p≅q
Parallel Postulate
If there is a line and point not on the line, then there is exactly 1 line through the point parallel to the given line
Perpendicular Postulate
If there is a line and point not on the line then there is exactly 1 line through the point perpendicular to the given line
Corresponding Angles Postulate
If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Alt. Interior Angles Theorem
If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Alt. Exterior Angles Theorem
If 2 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
Alt. Interior Angles Converse
If two lines are cut by a transversal so the alternate interrior angles are congruent, then the lines are parallel
Alt. 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
Slope
y₂-y₁/x₂ -x₁
Slope Intercept form
mx +b=y
Standard Form
Ax + By= C
Point Slope Form
y-y₁=m(x-x₁)
Steep slope reminder
The absolute value of the slope, pick the higher one
Shortest distance between any 2 parallel lines
lies a ⊥ distance
If 2 lines intersect to form a linear pair of ≅ angles
then the lines are ⊥ (linear pair)
If 2 lines are ⊥
then they intersect to form 4 right angles
If 2 sides of 2 acute adjacent angles are ⊥
then the angles are complementary
Perpendicular Transversal Theorem
If a transversal is ⊥ to one of 2 parallel lines, then it is ⊥ to the second line
Lines ⊥ to a Transversal Theorem
In a plane, if 2 lines are ⊥ to the same line then the lines are parallel to one another
Slope of Parallel lines
They have the same slope
Slope of ⊥ (perpendicular) lines
product of Slopes have to equal -1, reciprocal and reverse sign