Geometry unit 2
1,3,5,7,9,11,______
13
Theorem
A statement or conjecture that can be proven by undefined terms, definitions, postulates, and previously proven theorems
conjunction
a compound logic statement made up of two statements joined together with the word "and"
Reflexive Property of Congruence
a geometric property that states that a geometric figure to itself
Symmetric Property of Equality
an algebraic property that states that if one expression equals a second expression, then the second expression equals the first expression (a=b, then b=a)
Informal proof
an argument that uses logic without written justification to show that a conclusion is true
0,5,2,7,4,9,6,_________
11
2,4,8,16,32,64,_________
128
1,3,6,10,15,21,28,_________
36
algebraic proof
Proof that uses algebraic properties to reach a conclusion about an algebraic equation
If x=y then y=x
Symmetric property of equality
Distributive Property of Equality
an algebraic property that states that the product of one expression multiplied by the quantity of the sum of a second and third expression is equal to the sum of the quantity of the product of the first and second expression and the quantity of the product of first and third expression | a(b+c)=(ab)+(ac)
Commutive property of multiplication
an algebraic property that states the order in which expressions are multiplied does not change the final product (ab=ba)
valid argument
an application of deductive reasoning such that the reasoning is logically correct and undeniably true
proof
an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true
Formal proof
an argument that uses written justification in the form of definitions, properties, and previously proved geometric principles to show that a conclusion is true
Geometric proof
an argument that uses written justification in the form of definitions, properties, postulates, and previously proved theorems and corollaries to show that a conclusion is true
Counterexample
an example that proves that a conjecture or statement is false
If an angle is acute, then its measure is less than 90 degrees.
and angle is acute if, and only if, it is less than 90 degrees.
congruent angles
angles with the same measure
if two angles are vertical angles, then they are not adjacent angles
converse: if two angles are not adjacent angles, they are vertical. inverse: if two angle are not vertical they are adjacent. contrapositive: If two angles are adjacent angles, then they are vertical
5(a+b)=5a+5b
distributive property of equality
reasoning
the act of forming conclusions based on available information
related conditional statements
the converse, inverse, and contrapositive of a conditional statement
truth value
the degree of truth of a conditional statement
negation
the negative form of any part of a conditional statement
Conclusuion
the part of a conditional statement that expresses the action that will return if the conditions are met
inductive reasoning
the process of reasoning that a rule, condition, definition, property, or statement is true because specific cases have been observed to be true
if the same expression is added to both sides of an equation, then both sides of the equation remain equal.
the same expression is added to both sides of an equation if and only if both sides of the equation remain equal.
3*10=30 abd 30=5*6 so 3*10=5*6
transitive property of equality
Commutative Property of Addition
an algebraic property that states that the order in which expressions are added does not change the final sum (a + b = b + a)
Addition Property of Equality
an algebraic property that states that if the same expression is added to both sides of an equation, the two sides of the equation, the two sides of the equation remain equal
Subtraction Property of Equality
an algebraic property that states that if the same expression is subtracted from both sides of an equation, the two sides of the equation remain equal
Right Angle Congruence Theorem
All right angles are congruent
(3x)y=3(xy)
Associative property of multiplication
x+9=9+x
Commutative property of addition
2(4+5)=2(4)+2(5)
Distributive property of equality
assosiative property of multiplication
an algebraic property that states that in a given expression in which two or more addition operations are carried out in a row, the sum will be the same regardless(ab)c=a(bc)
I will pass geometry if i complete my homework correctly.
I will pass my geometry if, and only if, I do my homework correctly.
Congruent Complements Theorem
If two angles are complementary to the same angle or complementary to two congruent angles then the two angles are congruent
Congruent Supplements Theorem
If two angles are supplementary to the same angles to the same angles or supplementary to two congruent angles, then the two angles are congruent
Linear Pair Theorem
If two angles form a linear pair, they are supplementary.
x=y, so 4x=4y
Multiplicative property of equality
assosiative property of addition
an algebraic property that states that if the same expression is added or both sides of an equation, the two sides of the equation remain equal (a+b)+c=a+(b+c)
Justification
The statement of equality the reason for each step in proof
definition
a biconditional statement that is used to describe a geometric object or concept
Transitive Property of Congruence
a geometric property that states that if one geometric figure is congruent to a second figure, and the second figure is congruent to a third figure, then the first figure is also congruent to the third figure
Symmetric Property of Congruence
a geometric property that states that if one geometric figure to a second figure, then the second figure is congruent to the first figure
Law of Syllogism
a law of deductive reasoning that allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement
Law of Detachment
a law of deductive reasoning that states that if a conditional statement is true and its hypothesis is true, then its conclusion will also be true
bioconditional statement
a logical statement formed by the combination of a conditional statement and its converse
expression
a number, symbol, or group of numbers and/or symbols with their operations used to express so mathematical fact, quantity, or value
Hypothesis
a part of a conditional statement that expresses the conditions that must be met by the statement
geometric property
a property that compares the congruence of one geometric figure with the same or another geometric figure
contrapositive of a conditional statement
a related conditional statement in which the hypothesis and the conclusion of a conditional statement have been exchanged
inverse of a conditional statement
a related conditional statement resulting from the negation of the hypothesis and conclusion of a conditional statement
argument
a series of reasons that leads to conclusion
conjecture
a statement concluded to be true based on logical reasoning
conditional statement
a statement in which a conclusion is true if the conditions of a particular hypothesis are true
algebraic property
a universally accepted statement about an algebraic expression or equation that holds true in every instance in which the conditions of the property are met
Reflexive Property of Equality
an algebraic property that states that an expression is equal to itself
Division Principle of Equality
an algebraic property that states that if each side of an equation is divided by the same nonzero number, the two sides of and equation remain equal
Multiplication Property of Equality
an algebraic property that states that if each side of an equation is multiplied by the same expression, the two sides of the equation remain equal
Transitive Property of Equality
an algebraic property that states that if one expression equals a second expression, and the second expression equals a third expression, then the first expression also equals the third expression (a=b and b=c, then a=c)
Subsitution Property of Equality
an algebraic property that states that if one expression equals a second expression, the second expression can be substituted for the first expression in any expression