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