Points, Lines, & Planes
This geometric term is an undefined location that has neither shape nor size and is named by a single capital letter.
What is a point?
A measurable part of a line that consists of two endpoints and all the points between them.
What is a line segment
The point that is exactly halfway between the endpoints of a segment, dividing it into two congruent segments.
What is a midpoint?
Two angles whose measures have a sum of 90^\circ.
What are complementary angles?
The part of a conditional statement that follows the word "if."
What is the hypothesis?
Points that lie on the same line.
What are collinear points?
This is the length of a segment on a number line, calculated by finding the absolute value of the difference between the coordinates: PQ = \lvert x_2 - x_1 \rvert.
What is distance?
Any segment, line, plane, or point that intersects a segment at its midpoint.
What is a segment bisector?
The pair of non-adjacent angles created when two lines intersect, guaranteeing they are congruent.
What are vertical angles?
The statement formed by exchanging the hypothesis and the conclusion of the original conditional statement.
What is the converse?
This is a flat surface made up of points that extends infinitely, and you need at least three noncollinear points to name it
What is a plane?
The principle that states if Point C is between A and B, then AC + CB = AB
What is the Segment Addition Postulate (or Betweenness of Points)?
The process of making an educated guess or general rule (conjecture) based on observing patterns in specific examples.
What is inductive reasoning?
The principle that states if Point C is between A and B, then the length of the segments can be added: AC + CB = AB
What is the Segment Addition Postulate?
A single true statement that combines a true conditional and its true converse using the phrase "if and only if."
What is a biconditional statement?
The set of all points that two distinct planes share.
What is a line?
Segments that have the same length.
What are congruent segments?
A specific example that proves a generalized rule or conjecture is false.
What is a counterexample?
Two adjacent angles that form a straight line, meaning they are supplementary.
What is a linear pair?
The Law of Logic that allows you to conclude If p then r is true if both If p then q and If q then r are true.
What is the Law of Syllogism?
Points, lines, and planes are considered this because they are usually readily understood and not formally defined using more basic words.
What are undefined terms?
This formula is used to find the distance between two points (x_1, y_1) and (x_2, y_2) on a coordinate plane.
What is the Distance Formula?
The process of using facts, definitions, accepted properties, and the laws of logic to reach a specific, logical conclusion.
What is deductive reasoning?
The segment, line, or plane that intersects a segment exactly at its midpoint.
What is a segment bisector?
The statement created by negating both the hypothesis and the conclusion of the original conditional statement.
What is the inverse?