Geometry Chapter 1

A postulate is what?

A basic truth

An axiomatic system is a set of what?

Axioms

What is the first step in copying a line segment?

Draw a point that is not on the line

What do you not need to do for geometric construction?

Measure numbers

Which of the following is not an undefined term in geometry?

Quadrilateral

What is the negation of 'Triangles are not squares'?

Triangles are squares.

A ray has how many endpoints?

1

Which of the following is the correct symbol for a line?

<-ab->

Axioms are what?

Basic truths

What did Euclid say about circles?

Circles can be described with a point and a radius.

In geometry, which form of reasoning is relied more on for correct conclusions?

Deductive

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

If z = xy, then z = 2.

Which type of reasoning gives you hypotheses?

Inductive

What does the statement, 'We will go get ice cream if and only if you clean your room' mean?

It means no clean room, then no ice cream.

If someone asked you to choose between two candidates for president, but there were still five candidates running for president, what kind of logical fallacy is that?

Limited choice

What is the relationship between Angle 1 and Angle 7?

None of these answers are correct

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

then pq is odd.

Which of the following is the correct notation for a set?

{s, S}

If 4 = y and y = z, what does z equal?

4

Any line can also be what?

A number line

Which property tells us that we can add and multiply numbers in any order?

Commutative

Who invented the Cartesian coordinate system?

Descartes

Which of these is 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.

Which is the correct definition of a disjunction?

It is when two statements are connected with an 'OR'. The combined compound statement can be labeled as true when just one of the statements is true.

Which of the following is the correct way of writing a point?

P

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

Quadrilaterals

For any two points, how many lines will pass through both points?

1

Given the figure below, Angle 3 = 140y and Angle 5 = 80y + 70. Determine the value of y.

1/2

Consider the figure below, where Angle 4 = 12m - 4 Angle 5 = 10m + 20 Calculate the measure of Angle 5.

140 degrees

A line segment has how many endpoints?

2

What is the distance of this line segment?

2

The earliest written record of geometry dates back to when?

2000 BC

At least how many points are needed to make a plane?

3

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

Which of the following is the commutative law?

3 + 4 = 4 + 3

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

5

What is the total distance of four line segments that measure 1, 2, 2, and 3 inches respectively?

8 inches

If a = c and b = c, what kinds of new statements can you make? A: If a = c and b = c, then a = b. B: If a = 1, then b = 1. C: If b = 2, then a = 1.

A and B

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

What is a 'given' statement?

A statement provided as a part of the question.

Which of the following connectors is the logical conjunction?

AND

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.

Which of the following occurs with a direct proof?

All are correct

What is the relationship between Angle 2 and Angle 7?

Alternate exterior angles

Which of the following is Thales' Theorem?

An angle inscribed in a half-circle will be a right angle.

Which type of logical fallacy is illustrated in the example below? I will get an A in math class because I spent many sleepless nights studying.

Appeal to emotion

Which type of logical fallacy is illustrated below? The moon is made of cheese because it looks like cheese and no one has ever eaten the moon.

Appeal to ignorance

Which type of logical fallacy is illustrated below? Everyone in the class agrees that if x = 2 and y = 2, then x must equal y.

Appeal to popularity

Which type of logical fallacy is illustrated below? This chocolate pie must be bad because nobody is taking it.

Appeal to popularity

Which of the following tools is used in geometric construction?

Compass

A system that can prove or disprove any statement is what kind of system?

Complete

All of the following are used in geometric proofs EXCEPT:

Conjecture

A consistent axiomatic system does not do what to itself?

Contradict

What is the next step in copying angle BAC?

Draw an arc that intersects AB and AC

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

Drew likes roses and Drew loves lilies.

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

Euclid

Deductive reasoning is based on what?

Facts

What kind of reasoning does the statement below illustrate? My phone starts to ring whenever my cat starts to purr.

False cause

What kind of reasoning uses two unrelated events to prove a point?

False cause

Both Thales and Pythagoras are what?

Greek

What kind of logic is presented below? Your dog loves rock and roll music because my dog loves rock and roll music.

Hasty generalization

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.

What is the basis for all of Euclid's geometry?

His five axioms

Which of the following is 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.

Which of the following is 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.

If the following two propositions are true, which is a true statement? Theresa loves dogs. Spot is a dog.

If Spot is a dog, then Theresa loves Spot.

Which of the following is a conditional statement?

If a square is a rectangle, then a triangle is a shape.

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

If all mammals are animals

All of the following statements could be proven with a direct proof EXCEPT:

If n is an odd integer, then m is an even integer.

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

Which of the following is a conditional statement?

If the dog barks, then the cat will meow.

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.

All rays start at a point and have a length measurement of _____.

Infinity

Which is the correct definition of a conjunction?

It is when two statements are connected with an 'AND'; only when both statements are true is the resulting compound statement true.

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.

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

Not independent

Which of the following connectors is the logical disjunction?

OR

Inductive reasoning is reasoning based on what?

Observations

The intersection of two planes looks like what?

One line

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

Pythagoras

In a 2-column proof, what goes in the column on the right?

Reasons

Which law is shown by the following? x = x

Reflexive

What is an example of a logical fallacy?

Saying something is true or false based on emotions

What is geometry about?

Shapes

Geometry is the study of what?

Shapes and space.

In a 2-column proof, what goes in the column on the left?

Statements

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

Switching the hypothesis and the conclusion.

Which law tells you that if x = 7, then 7 = x?

Symmetric

Euclid wrote which textbook?

The Elements

Which of these is always logically equivalent to the inverse?

The converse

What part of the pyramid was Thales able to calculate?

The height

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.

Which statement is an example of circular reasoning?

The moon is made of cheese because the moon is made of cheese.

Which of the following is the Pythagorean Theorem?

The square of the hypotenuse of a right triangle is equal to the sum of the square of the two other sides.

A statement can be determined to be which of the following through a direct proof?

True or false

Which of the following is not one of the five axioms?

Two intersecting lines create equal vertical angles.

What is the relationship between Angle 4 and Angle 1?

Vertical angles

All of the following are recommended steps when completing geometry proofs EXCEPT:

Write the steps in paragraph form

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

p: T q: F

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 q: T