Lines and Angles
A set of points consisting or two different rays that have the same endpoint (called the vertex).
What is an angle?
It states that if there is one line and a point not on the line, then there is exactly one line through the given point parallel to the given line.
What is the parallel postulate?
a = a
AB = AB
What is the reflexive property?
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
What is the corresponding angles theorem?
An unproven statement based on observations.
What is conjecture?
Two lines that do not intersect and are coplanar.
What are parallel lines?
It states that there is exactly one line through point P perpendicular to line l.
What is the perpendicular postulate?
If a = b, then b = a
If AB = CD, then CD = AB
What is the symmetric property?
It says that segment congruence is reflexive, symmetric, and transitive.
What is the properties of segment congruence theorem?
A specific case for which the conjecture is false.
What is a counterexample?
A line that intersects two or more coplanar lines at different points.
What is a transversal?
It states that a line contains at least two points.
What is the line-point postulate?
If a = b and b = c, then a = c
If AB = CD and CD = EF, then AB = EF
What is the transitive property?
It states that angle congruence is reflexive, symmetric, and transitive.
What is the properties of angle congruence theorem?
This is when you find a pattern in specific cases and then write a conjecture for the general case.
What is inductive reasoning?
It states that if two lines are parallel to the same line, then they are parallel to each other.
What is the transitive property of parallel lines theorem?
It states that if two angles form a linear pair, then they are supplementary.
What is the linear pair postulate?
These are line segments with the same length.
What are congruent segments?
It states that vertical angles are congruent.
What is the vertical angles congruence theorem?
This uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.
What is deductive reasoning?
Two angles that lie between the two lines and on opposite sides of the transversal t.
What are alternate interior angles?
It states that the points on lines can be matched one to one with real numbers. The real number that matches to a point is the coordinate of a point.
The distance between points A and B, written as AB, is the absolute values of the difference of the coordinates of A and B.
What is the ruler postulate?
It is a point, ray, line, line segment, or plane that intersects a segment at its midpoint.
What is a segment bisector?
A statement that can be proven. Once it has been proved, you can use it as a reason in other proofs.
What is a theorem?
A logical argument that uses deductive reasoning to show that a statement is true.
What is a proof?