Chapter 2&3 Flashcards
Postulate about planes
Three points determine a plane
Has at least three non collinear points
Two points in a plane, the likes with the points lie in the plane
If two points intersect the intersection is a line
Postulates about lines
Two points determine a line
A line contains two points
If two lines intersect the intersection is a point
Perpendicular
Two lines that meet at a right angle
Addition property of equality
a+c=b+c
Subtraction property of equality
a-c=b-c
Multiplication property of equality
A(c)=b(c)
Division property of equality
A/c=b/c
Substitution property of equality
A can be substituted for B In any equation or expression
Distributive property
a(b+c)=AB+BC
Reflexive property of equality
A=A a thing equals to itself
Symmetric properties of equality
A=b, then b=a
If one expression equals another, it doesn’t matter which expression foes on which side
Transitive properties of equality
If a=b and b=c, then a=c
If two things equal a third thing, they also equal each other
Right angle congruence theorem
All right angles are congruent
Vertical angles congruence theorem
All vertical angles are congruent
Linear pair postulate
Angles in a linear pair are supplements
Parallel lines
Don’t intersect and slopes are equal
They can be on a plane
A line can be parallel to a plane if it is on the plane or on another plane that’s parallel
Skew lines
Do not intersect and are not on the same plane
Parallel postulate
Given a line and a point not on the line, you can draw only one line that is parallel to the original line and goes through the point.
Perpendicular postulate
Given a line and a point not on the line, you can draw only one line that is perpendicular to the original line and goes through the point.
Transversal
A line that intersects two or more other limes at different points
Interior angles
Inside the lines
Exterior angles
Outside the lines
Consecutive angles
Same side of the transversal
Alternate angles
Opposite sides of transversal
Consecutive interior angles postulate
parallel lines crossed by a transversal, consecutive interior angles will always be supplementary
Alternate Interior Angles Postulate
parallel lines crossed by a transversal, alternate interior angles are always congruent
Alternate Exterior Angles Postulate
parallel lines crossed by a transversal, alternate exterior angles are congruent.
Corresponding Angles Postulate
Parallel lines crossed by a transversal, corresponding angles are congruent
Consecutive Interior Angles Converse Theorem
If their consecutive interior angles are supplements then the lines are parallel.
Alternate interior angles converse theorem
if their alternate interior angles are congruent, then the lines will be parallel.
Alternate exterior angles converse theorem
if their alternate exterior angles are congruent, then the lines will be parallel.
Corresponding angles converse theorem
if their corresponding angles are congruent, then the lines will be parallel
Transitive property of parallel lines
If A is parallel to B and B is parallel to C then A and C are parallel.
Slopes of parallel lines
If two lines are parallel, then they have the same slope
If two lines have the same slope, then they are parallel
Vertical lines have no slope, but they are always parallel to each other
Slopes of perpendicular lines
If two lines are perpendicular to each other, their slopes are opposite and reciprocal to each other
If two lines have the slope that is opposite and reciprocal of each other, they are opposite of each other.
Vertical lines are always perpendicular to a horizontal line.
Perpendicular Transversal Theorem
if a transversal us 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.
