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Chapter 2 Geometry (Holt McDougal) Geometric Reasoning Key Terms/Postulates

Terms in this set (29)

Linear Pair Theorem
If two angles form a linear pair, then they are supplementary.
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or two congruent angles), then the two angles are congruent.
Right Angle Congruence Theorem
All right angles are congruent.
Congruent Complements Theorem
If two angles are complementary to the same angle (or to two congruent angles), then the two angles are congruent.
Common Segments Theorem
Given collinear points A, B, C, and D, if line segment AB≅ line segment CD, then line segment AC≅ line segment BD.
Vertical Angles Theorem
Vertical angles are congruent.
inductive reasoning
The process of reasoning that a rule or statement is true because specific cases are true.
conjecture
A statement that is believed to be true.
counterexample
An example that proves that a conjecture or statement is false.
conditional statement
A statement that can be written in the form, "if p, then q," where p is the hypothesis and q is the conclusion.
hypothesis
The part of a conditional statement following the word "if."
conclusion
The part of a conditional statement following the word "then."
truth value
A statement can be either true (T) or false (F).
negation
For p, this makes the statement "not p," written as ~p.
converse
The statement formed by exchanging the hypothesis and conclusion of a conditional statement.
inverse
The statement formed by negating the hypothesis and conclusion of a conditional statement.
contrapositive
The statement formed by exchanging and negating the hypothesis and conclusion of a conditional statement.
logically equivalent statements
Statements that have the same truth value.
deductive reasoning
The process of using logic to draw conclusions.
biconditional statement
A statement that can be written in the form "p if and only if q." (p iff q.)
definition
A statement that describes a mathematical object and can be written as a true biconditional statement.
polygon
A closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear.
triangle
A three-sided polygon.
quadrilateral
A four-sided polygon.
proof
An argument that uses logic to show that a conclusion is true.
theorem
A statement that has been proven.
two-column proof
A style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column.
flowchart proof
A style of proof that uses boxes and arrows to show the structure of the proof.
paragraph proof
A style of proof in which the statements and reasons are presented in paragraph form.
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