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An unproven statement based on observations 


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An example that shows the conjecture is false. 


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3 or more points that lie on the same line. 


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4 or more points that lie on the same plane. 


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Two rays that connect at a middle point. 


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A rule that is accepted without proof. 


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Points on a line that can be matched up with real numbers. 


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Segment Addition postulate 

Definition
If B is between A and C, then AB + BC = AC 


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Segments that have the same length. 


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Two rays with the same initial point. 


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Angles that have the same measure. 


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Each angle has a measure from 0 degrees to 180 degrees. 


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Share a common vertex and a common interiorside. 


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The point that divides the segment into two congruent parts. 


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Any segment, ray, line of plane, that goes through the midpoint of a segment. 


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A ray that divides an angle into two congruent adjacent angles. 


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Angles whose sides form two pairs of opposite rays 


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Two adjacent angles that form a straight line. 


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Two angles whose sum is 90 degrees 


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Two angles whose sum is 180 degrees. 


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Two lines that intersect and form a right angle. 


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Line perpendicular to a plane 

Definition
A line that intersects a plane in a point 


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Definition
If p>q is true, and p is true, then q is true. 


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Law of syllogism (Transitivity) 

Definition
If p>q and q>r, are both true,then p>r is true. 


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Law of the contrapositive 

Definition
If a conditional p>q is true, then it's contrapositive, ~q>~p is also true. 


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If you know the value of a variable, then you can plug it in. 


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A statement that follows as a result of other true statements. All theorems must be proven in order to be considered a theorem. 


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Right angle congruence theorem 

Definition
All right angles are congruent 


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Congruent Supplements Theorem 

Definition
If two angles are supplementary to the same angle, then they are congruent to each other. 


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Congruent complements theorem 

Definition
If 2 angles are complementary to the same angle, then they are congruent to each other. 


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Definition
If 2 angles form a linear pair, then they are supplementary. 


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If two angles are vertical angles, then they are congruent. 


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Coplanar lines that never intersect 


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Lines in different planes that never intersect 


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Planes that don't intersect 


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If there is a line and a point not on a line, then there is one line through the point parallel to the given line. 


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If there is a line and a point not on the line, then thereis one line through the point perpendicular to the given line. 


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If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. 


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If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 


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If two lines are perpendicular, then they intersect to form four right angles. 


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A line that intersects coplanar lines in two or more different points. 


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Corresponding Angles postulate 

Definition
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 


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Alternate interior angles theorem 

Definition
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent 


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Consecutive Interior angles theorem 

Definition
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 


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Alternate exterior angles theorem 

Definition
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 


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Perpendicular to parallels theorem 

Definition
If a transversal is perpendicular to one of two paralllel lines, then it is perpendicular to the other. 


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Corresponding angles converse postulate 

Definition
If two lnes are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 


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Alternate interior angles converse theorem 

Definition
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 


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Consecutive interior angles converse theorem 

Definition
If two lines are cut by a transversal so that consecutive ihnterior angles are supplementary , then the lnes are parallel. 


Term
Alternate exterior angles converse theorem 

Definition
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. 


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Transitivity of Parallels theorem 

Definition
If two lines are parallel to the same line, then they are parallel to each other. 


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Two perpendiculars Theorem 

Definition
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. 

