State the theorem
Vertical Angles Congruence Theorem
If B is between A and C, then AB + BC = AC
Segment Addition Postulate
Perpendicular Postulate:
If there is a line and point not on the line, then there is exactly one line through the point ____________ to the given line.
two angles with the same angle measures
congruent angles
Conditional Statement: a logical statement that has two parts, a ______________ and a ___________.
hypothesis, conclusion
If two angles are supplementary to the same angle, then they are congruent.
Congruent Supplements Theorem
If two angles form a linear pair, then they are supplementary
Linear Pair Postulate
Line-Point Postulate:
A line contains at least ____ _______.
two points
point, ray, line, line segment, or plane that intersects the segment at its midpoint
segment bisector
midpoint: a point that divides the segments into ___ _____ ________.
two congruent segments
Segment Congruence are reflexive, symmetric, and transitive.
Properties of Segment Congruence
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.
Parallel Postulate
Two Point Postulate:
Through any two points, there exists _____ ______ _________.
exactly one line
two lines that do not intersect and are coplanar
parallel lines
counterexample: a specific case for which the ________ is false.
conjecture
If two lines are parallel to the same line, then they are parallel to each other
Transitive Property of Parallel Lines
If two lines intersect, then their intersection is exactly one point.
Line Intersection Postulate
Through any ______ _______ _______, there exists exactly one plane,
three noncollinear points
two adjacent angles whose uncommon sides are opposite rays
linear pair
theorem: a _______ that can't be proven
statement
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel
Alternate Exterior Angles Converse
If two points lie in a plane, then the line containing them lies in the plane.
Plane-Line Postulate
Angle Addition Postulate
If P is in the interior of ∠RST, then the measures of ∠RST is the equal sum to the measures of ∠______ and ∠_____________
∠RSP and ∠PST
two angles that lie between the two lines and on opposite sides of the transversal
alternate interior angles
Law of Detachment: If the hypothesis of a _____ _____ ________, then the conclusion is also true.
true conditional statement