geometry

1.8 associative law: 1(2 x 3) is the same as

(1 x 2)3

1.7 for any two points, how many lines will pass through the points?

1

1.7 any line can also be what?

a number line

1.8 what are algebraic laws?

laws that tell us how things add, subtract, multiply, divide, and otherwise combine together

1.4 the axioms in an axiomatic system are said to be independent if

the axiom cannot be derived from the other axioms in the system. however, an axiomatic system can be either independent or dependent, so this is not a requirement for an axiomatic system

2.5 what is always logically equivalent to the inverse?

the converse

1.3 what part of the pyramid was Thales able to calculate?

the height

1.2 What conclusion can be reached using inductive reasoning from the following? When the sun comes up, the rooster crows. When the rooster crows, the hen lays an egg. What happens when the sun comes up?

the hen lays an egg

2.5 what is logical equivalence?

the mutually supported logic between two statements

1.4 the fifth axiom of EG states that if a line intersecting two lines forms interior angles less than 90 degrees, then the two lines will intersect on the same side as the angles that are less than 90 degrees. what is this called?

the parallel postulate

1.2 what is deductive reasoning

the process of reaching conclusions based on previously known facts. these are valid and can be relied on

2.1 what is logic?

the study of how to critically think about propositions

1.7 what are the building blocks of geometry?

the three postulates- point, line and plane

2.6 What is the conclusion in the following statement? 'If p and q are odd integers, then pq is odd.'

then pq is odd

2.1 when do you use critical thinking?

to make new connections based on what you know to be true

2.2 what is the negation of triangles are not squares?

triangles are squares

2.5 statements which are logically equivalent both contain the same ___ and ___

truth value and logical content

1.3 Pythagoras said that the three angles of a triangle will add up to what?

two right angles, or 180 degrees

1.8 distributive law: 2(3+4) equals

2 x 3 + 2 x 4

1.1 The earliest written record of geometry dates back to when?

2000 bc

1.7 at least how many points are needed to make a plane?

3

1.8 transitive law: if x = y and y=3 then x=??

3

2.2 How many propositions are there in the statement below? I will buy you a huge bacon cheeseburger and wash your car if and only if you give me your big screen television.

3 (1) I will buy you a huge bacon cheeseburger, 2) I will wash your car, and 3) you give me your big screen television.)

1.5 How many basic truths did Euclid establish as the basis for geometry?

5

1.6 what is the symbol for a line?

<--> AB

2.1 Which of the following is a logic proposition? A: Sam only eats square foods B: Once upon a time C: Circles roll

A and C

2.3 Which is a correct logical disjunction formed with the following phrases? Algebra is easy. Geometry is a breeze.

Algebra is easy or geometry is a breeze.

2.5 Write the inverse of the below argument: If I am in Kansas, then I'm in the United States.

If I'm not in Kansas, then I'm not in the United States.

2.4 Write a conditional statement whose hypothesis is 'Joe has a red car' and whose conclusion is 'Billy gets to drive it'?

If Joe has a red car, then Billy gets to drive it.

2.5 Write the logical contrapositive to the following statement? If killing in any sense is wrong, then murder is wrong.

If murder is not wrong, then killing in any sense is not wrong.

2.6 What is the hypothesis in the following statement? 'If p is an even integer and q is an odd integer, then p + q is an odd integer.'

If p is an even integer and q is an odd integer

If Jimmy does his chores, then Jimmy will get a big scoop of chocolate ice cream. Which of the following represents the conclusion in the above conditional statement?

Jimmy will get a big scoop of chocolate ice cream.

1.1 what is euclidean geometry based on?

a collection of basic truths and definitions presented in Euclid's Elements

1.4 what is a axiomatic system?

a set of axioms used to derive theorems. What this means is that for every theorem in math, there exists an axiomatic system that contains all the axioms needed to prove that theorem

1.4 what is an axiom?

a statement that is considered true and does not require a proof. It is considered the starting point of reasoning. Axioms are used to prove other statements. They are basic truths

2.2 what is a truth table?

a table showing all the truth values for logic combinations

2.5 In the following statement, which part is the hypothesis? If all mammals are animals, then dogs are animals.

all mammals are animals

1.3 What is Thales Theorem?

an angle that is inscribed inside a semicircle will be a right angle

2.4 conditional statements have what kind of structure?

an if-then structure (if this happens, then this will occur).

2.2 what are the four logic combinations?

and, or, if-then, and if-only if.

2.3 when you have two statements and you want to combine them you can add either an "___" or an "___" between the two statements. These are called:

and; or; these are called connectors

1.4 the first axiom of Euclidean Geometry states that a straight line can be drawn from?

any one point to any other point.

2.3 what are statements?

any phrase that can be labeled as either true or false

1.8 symmetric law: 3 = b is the same as

b = 3

1.7 what are postulates?

basic truths that do not require formal proofs to prove that they are true.

1.3 Thales concluded that the diameter of a circle does what?

bisects, or cuts, the circle in half

1.4 the third axiom of EG states that a circle can be described with a ___ and ___

center and radius

1.1 if two triangles have two equal sides and the angle in between the two sides is equal, then the two triangles are...

congruent

1.3 Thales concluded that when two triangles have two equal angles and one equal side, then they are ____ to each other

congruent (equal)

2.3 When two statements are connected with an 'and,' you have a

conjunction (both statements must be true)

1.4 what are the three properties of axiomatic systems?

consistency, independence, and completeness

2.5 When trying to determine whether or not a statement is logically true, it can be useful to employ a ______ , or an easily understood substitute to examine the validity of the logic.

counterexample

1.4 If an axiom can be proved by the other axioms in a system, then the axiom is what?

dependent

2.3 when two statements are connected with an 'or' you have a

disjunction (only one statement is true)

1.8 distributive law states that if we mix multiplication and addition along with a pair of parentheses like x(y+z), then the x

distributes to the y and z. x(y + z) = xy + xz

1.6 undefined terms are words that

dont require a formal definition

2.3 Which is a correct logical conjunction formed with the following phrases? Drew likes roses. Drew loves lilies.

drew likes roses and drew loves lilies

1.4 a complete axiomatic system is a system where for any statement...

either the statement or its negative can be proved using the system. if there is any statement the system cannot prove or disprove, then the system is not complete. it is not a required property.

1.3 Thales concluded that the base angles of an isosceles triangle are ___ to each other

equal

1.3 Thales concluded that when you have two straight lines intersecting each other, the opposite or vertical angles are ___ to each other

equal

1.4 the fourth axiom of EG states that all right angles are

equal to each other

1.1 Whose system of definition and proofs do we still use today?

euclid

1.3 both Thales and Pythagoras are what?

greek

2.4 If he eats a hamburger, then he will eat two bags of fries. Which of the following represents the hypothesis in the above conditional statement?

he eats a hamburger

1.5 what is the basis for all of Euclid's geometry?

his five axioms

2.4 what are the two parts of an conditional statement? when do they occur within the statement?

hypothesis and conclusion. the hypothesis comes after the 'if' and before the comma. the conclusion comes after the 'then' and before the period. a conditional statement will look like this: if HYPOTHESIS, then CONCLUSION

2.6 the direct proof is a series of statements that start with the ___ and then use known facts and processes to determine _________

hypothesis, the truth of the conclusion

1.8 transitive law tells us

if one item equals a second item and the second item equals a third, then the first item also equals the third item

1.8 symmetric law tells us that

if one variable equals another, then the other variable equals the first.

2.1 Triangles have 180 degrees in total, and squares are two triangles put together. What can you say about the total degrees of a square?

if triangles have 180 degrees in total, then squares have 360 degrees in total

2.1 If x = 1 and y = 2, what can be said about z if z = xy?

if z = xy. then z = 2.

1.2 what are the two fundamental forms of reasoning for mathematicians?

inductive and deductive reasoning

1.4 the second axiom of EG states that a line segment can be extended

infinitely in both directions

2.6 what is a direct proof?

method of showing whether a conditional statement is true or false using known facts and rules.

2.2 what changes a truth value?

negating a proposition

2.5 the logical contrapositive of a conditional statement is created by

negating the hypothesis and conclusion, then switching them

2.5 the inverse of the original statement is the

negative form of the conditional in which both hypothesis and conclusions are negated

1.4 when an axiom is consistent, then the system will...

not be able to prove both a statement and its negotiation. if it did, it would contradict itself. this is a requirement.

1.7 the intersection of two planes looks like what?

one line

1.7 for any three non-collinear points, there will be exactly

one plane that will pass through all three points

2.2 a negation is the __ of the original statement

opposite

1.7 postulates are used to prove what?

other theorems to be true

2.2 For the combination p AND (NOT q), for which truth values of p and q is the combination true? p: The pond is not frozen over. q: The fish are not jumping.

p: T and q: F

2.2 p: The dog rolls over on command. q: The dog gets a treat. For the combination p AND q, for which truth values of p and q is the combination true?

p: T and q: T

1.6 what are the four undefined terms in geometry?

point, line, plane, and set

1.1 Who invented the theorem that says the square of the hypotenuse equals the sum of the squares of the other two sides?

pythagoras

1.6 what shape is used to draw a plane on paper in geometry?

quadrilaterals

1.2 what is inductive reasoning?

reaching a conclusion based off of a series of observations. it may or may not be valid, but it gives you a hypotheses

1.1 who developed the cartesian coordinate system?

rene descartes

1.1 geometry is the study of what?

shapes and space

2.1 what are propositions?

simple statements that can either be true or false

2.5 the converse of the original statement is created by

switching the hypothesis and conclusion

2.5 The converse of a logical statement is found by doing what?

switching the hypothesis and the conclusion

1.3 Pythagoras was able to construct what shapes?

tetrahedron, cube, and octahedron

1.8 reflexive law tells us

that a number is equal to itself (1=1)

1.3 What does the Pythagorean Theorem state?

that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides

1.8 what does the cumulative law tell us?

that we can add and multiply numbers in whatever order we like. x + y = y + x and x * y = y * x.

1.8 associative law tells us that

we can add and multiply three numbers in any order. x + (y + z) = (x + y) + z and x(yz) = (xy)z

2.2 what is the truth value of a statement?

whether the statement is true or false

1.6 what is the correct notation for a set?

{s, S}