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Conditional Statements
Deductive Reasoning
Definitions and Biconditional Statements
Reasoning with Properties from Algebra
Proving Statements about Segments and Angles
100
A type of logical statement that has two major parts.
What is a conditional statement?
100
A symbol for negation which is written before the letter.
What is the ~ symbol?
100
Symbol that is read as "is perpendicular to."
What is the ⊥ symbol?
100
An example would be: AB=AB
What is the Reflexive Property of Equality?
100
All right angles are congruent.
What is the Right Angle Congruence Therom?
200
The two parts that make up a conditional statement.
What is a hypothesis and conclusion?
200
Something that uses facts, definitions, and accepted properties in a logical order to write a logical argument.
What is Deductive Reasoning?
200
Two lines intersect to form a right angle.
What are perpendicular lines?
200
An example would be the following: If BX=CY and CY=MG, then BX=MG.
What is the Transitive Property?
200
A type of proof written in the form of a paragraph.
What is a paragraph proof?
300
An example that shows a conjecture is false.
What is a counterexample?
300
If p->q is a true conditional statement and p is true, then q is true.
What is the Law of Detachment?
300
A line that intersects the plan in a point and is perpendicular to every line in a plane that intersects it.
What is a line perpendicular to a plane?
300
Converting H+P=72 and H+P+N=117 to 72+N=117 is an example.
What is the Substitution Property of Equality?
300
A true statement that follows as a result of other true statements.
What is a theorem?
400
When both statements are both true or both false.
What are equivalent statements?
400
If p->q and q->r are true conditional statements, then p->r is true.
What is the Law of Syllogism?
400
A statement that can be rewritten as a conditional statement and its converse.
What is a Biconditional Statement?
400
An example would be: If 7^2-17/3=18*n^7, then 18*n^7=7^2-17/3.
What is the Symmetric Property of Equality?
400
A list of sequential and logically ordered statements and reasons of an argument.
What is a two-column proof?
500
A statement can be altered by this, that is, by writing the negative of the statement.
What is negation?
500
Requires deductive reasoning in order to write.
What is a logical argument?
500
You score a touchdown if and only if the football crossed the goal line. -If you scored a touchdown, then the football crossed the goal line. -If the football crossed the goal line, then you scored a touchdown. (The last two statements)
What is a conditional statement and its converse.
500
An example would be: 2x(4x^2-9.7)=8x^3-19.4x
What is the Distributive Property of Equality?
500
If two adjacent angles whose noncommon sides are opposite rays, then they, together, form a 180 degree angle.
What is the Linear Pair Postulate?