Properties of Equality
Logic and Reasoning
Definitions
Theorems/Postulates
Conditional Statements
100
For every number a, a=a.
What is the reflexive property?
100
This unproven statement that is based on observations might also be called an educated guess.
What is a conjecture?
100
Given two segments are congruent, this definition tells me their measures are the same.
What is the definition of congruent segments?
100
If ray BD lies in the interior of angle ABC, then this postulate tells me that measure of angle ABD+measure of angle DBC=measure of angle ABC.
What is the angle addition postulate?
100
These pieces may be switch to find the converse of our original statement.
What are the hypothesis (p) and the conclusion (q)?
200
This property proves to me that if I have a=b, then I can also have b=a.
What is the symmetric property?
200
If you are using personal experiences then this reasoning will help you go from a specific experience to a general conclusion.
What is inductive reasoning?
200
If told B is the midpoint of segment AC, this definition tells me that segment AB is congruent to segment BC.
What is the definition of midpoint?
200
If <1 and <2 and complementary, and <2 and <3 are complementary, the I can conclude that <1 is congruent to <3.
What is the congruent complement theorem?
200
If we are given a statement like this, then it is called a ____ .
What is a conditional statement?
300
Paired together in most cases, I use these properties to "move" terms from one side of the equals sign to the other.
What are the addition and subtraction properties of equality?
300
If p -> q. Then q -> r. We can conclude that p -> r.
What is the law of syllogism?
300
Through this definition, if told <1 and <2 are supplementary, then I can conclude that m<1+m<2=180.
What is the definition of supplementary angles?
300
If <1 and <2 from a linear pair, this tells me those angles are supplementary.
What is the linear pair postulate?
300
If it is raining, then I will carry an umbrella. However, "If it is not raining than I will not carry an umbrella" would be called this.
What is the inverse?
400
If a=b, b=c, then this property tells me that a=c.
What is the transitive property of equality?
400
If the bell rings, then we will go to lunch. The bell rings. Using this law I know we will go to lunch.
What is the law of detachment?
400
If angle ABC is a right angle then it's measure is 90.
What is the definition of right angles?
400
If <1 and <2 are right angles, then I know these angles are congruent.
What is the right angle congruence theorem?
400
The contrapositive is formed by doing this to the ORIGINAL conditional statement.
What is both negating and switching the hypothesis and conclusion?
500
For all real numbers a and b, if a=b then "a" may be replaced by b in any equation or expression.
What is the substitution property?
500
Using laws, rules, or widely accepted principles, this reasoning allows us to take a general idea and apply it to our specific situation.
What is deductive reasoning?
500
Also written as a biconditional statement, this definition tells us that right angles are formed when a certain type of lines intersect.
What is the definition of perpendicular lines?
500
If angle 1 and angle 2 are vertical, then the fact they are congruent is formed from this theorem.
What is the vertical angle congruence theorem?
500
This is formed if and only if both the conditional statement and its converse are true.
What is a biconditional statement?
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