Geometry Study Guide (Unit 1)

Sarah solves the equation as shown. 2(x + 3) = 8 1. 2x + 6 = 8 2. 2x = 2 3. x = 1

1

If m and n are real numbers such that 4m + n = 10, then which of the following expressions represents m?

10 minus n, divided by 4

The mathematical expression 2 ∈ V means:

2 is an element of set V

The number of subsets that can be created from the set {1, 2, 3} is:

8

The mathematical expression 9 ∈ T means:

9 is an element of T

The mathematical expression 9 ∉ T means:

9 is not an element of T

set

A collection or group of objects.

A ⊂ B means:

A is a subset of B

What is indicated by arrowheads on a line?

A line extends indefinitely in both directions

union of sets

A set containing all elements of all sets being considered.

intersection of sets

A set containing elements in common for all sets being considered.

subset

A set that contains only elements found in another set.

empty set

A set that has no elements. It is sometimes called the null set.

proper subset

A subset that does not contain every element in another set.

Select the postulate that is illustrated for the real numbers. 25 + 0 = 25

Additive identity

Intersecting lines are _______ coplanar.

Always

element

An object that belongs to a set. Sometimes the word "member" is used.

finite set

Any set whose elements can be counted.

infinite set

Any set whose elements cannot be counted.

Which of the following best describes an indirect proof?

Assume a statement true and then show it must be false.

Select the postulate that is illustrated for the real numbers. 3 + 2 = 2 + 3

Commutative postulate for addition

disjoint sets

Sets that have no common elements.

Select the postulate that is illustrated for the real numbers. 5 + (-5) = 0

The addition inverse postulate

Select the postulate that is illustrated for the real numbers. 6 + 0 = 6

The additive identity postulate

complement of a set

The elements in the universe that are not in the set.

Al is taller than Bob, and Bob is taller than Carl. Which property would you use to prove that Al is taller than Carl?

Transitive property

Complete the conditional statement. If -2a > 6, then _____.

a < -3

Complete the conditional statement. If a + 2 < b + 3, then _____.

a < b + 1

Complete the conditional statement. If 2 > -a, then _____.

a > -2

A line can be named by using:

a lowercase letter

Which of the following would represent a line in the real world?

a pencil

In Geometry, "line" is _____.

an undefined term

Line over a letter

called a complement that means anything not in that letter

Points are usually labeled as:

capital letters

A point is represented by a:

dot

The empty set (or null set) is a subset of _____ set(s

every

Hilbert's axiom's changed Euclid's geometry by _____.

identifying and explaining the concept of undefined terms

How many points are contained on a line?

infinitely many

Which of the following is a subset of {1, 3, 5, 7, 9}?

integers between 1 and 9

Which is the characteristic of a line?

length

Which of the following attributes does a line have?

length

Two planes intersect in a _____.

line

A point represents a _____.

location

Points have the following physical properties: depth height thickness

none

Two intersecting lines have of point(s) -------- in common.

one

Which of the following options represent(s) the three undefined terms in geometry? Select all that apply.

plane,point,line

A line is a collection of __________.

points

What are axioms in algebra called in geometry?

postulates

Unless otherwise indicated, a line in geometry is understood to be _____.

straight

Select the property of equality used to arrive at the conclusion. If x - 3 = 7, then x = 10

the addition property of equality

Select the property of equality used to arrive at the conclusion. If x = 2, then x + 8 = 10

the addition property of equality

Select the property of equality used to arrive at the conclusion. If 5x = 20, then x = 4.

the division property of equality

Select the property of equality used to arrive at the conclusion. If x = 4, then 5x = 20

the multiplication property of equality

Which of the following is an infinite set?

the set of integers

Select the property of equality used to arrive at the conclusion. If x + 8 = 10, then x = 2.

the subtraction property of equality

Select the postulate of equality or inequality that is illustrated. 3 + 2 5 and 3 + 2 = 5 are not both true.

the symmetric postulate of equality

Select the postulate of equality or inequality that is illustrated. If 5 = x + 2, then x + 2 = 5

the symmetric postulate of equality

Select the postulate of equality or inequality that is illustrated. If a < b and b < 2, then a < 2

the symmetric postulate of equality

Select the postulate of equality or inequality that is illustrated. 5 = 5

the transitive postulate of inequality

A statement that is proved by deductive logic is called a ______.

theorem

Which of the following is proved by utilizing deductive reasoning?

theorems

How many points are used to define a plane?

three

What is the minimum number of intersecting lines that lay in a plane?

two

(x+2)(x+6)=0 In the problem shown, to conclude that x + 2 = 0 or x + 6 = 0, one must use the:

zero product property

Form the intersection for the following sets. E = {1, 2, 3} F = {101, 102, 103, 104} E ∩ F =

{ }

Form the intersection for the following sets. M = { } N = {6, 7, 8, 9, 10} M ∩ N =

{ }

Form the union for the following sets. E = {1, 2, 3} F = {101, 102, 103, 104} E ∪ F =

{1, 2, 3, 101, 102, 103, 104}

Which of the following is a subset of {1, 2, 3}?

{1, 2, 3}

Form the union for the following sets. X = {0, 10, 100, 1000} Y = {100, 1000} X ∪ Y =

{100, 1000}

Which is a subset of {1, 2, 4, 5, 6}?

{2, 6}

Form the intersection for the following sets. R = {10, 15, 20} S = {20, 25} R ∩ S =

{20}

Form the union for the following sets. R = {10, 15, 20} S = {20, 25} R ∪ S =

{20}

Form the union for the following sets. M = { } N = {6, 7, 8, 9, 10} M ∪ N =

{6, 7, 8, 9, 10}

The school has 800 students with 20 students on the gymnastic team and 10 students on the chess team (including 3 students who are on both teams). How many students in the school are not members of either the gymnastic team or the chess team?

{773}

Which of the following is proper notation to describe the set of all letters in the alphabet?

{a, b, c . . . z}