Euclidean Geometry

Question 1

Planes have _____ dimensions

Answer 1

2

Question 2

Lines have ______ dimensions

Answer 2

1

Question 3

Points have _______ dimensions

Answer 3

0

Question 4

A point is ______

Answer 4

A location represented by a dot with no length or width or thickness, named with a capital letter, undefinable

Question 5

A line is

Answer 5

A figure with length but no width, a series of points, extends indefinitely in both directions, named with two capital letters with a line on top or with one lowercase letter, undefinable.

Question 6

A plane is

Answer 6

flat surface made of infinite lines, extends in all directions, no thickness but length and width, named by a capital letter in script or three noncollinear points on the plane, undefinable

Question 7

definition

Answer 7

a formal statement declaring the meaning of a word

Question 8

postulate

Answer 8

a mathematical statement taken as fact (assumption)

Question 9

theorem

Answer 9

a mathematical statement proven using postulates and definition

Question 10

diagram

Answer 10

a visual tool representing mathematical ideas to be interpreted

Question 11

point existence postulate

Answer 11

a line contains at least two points

Question 12

collinear

Answer 12

on same line

Question 13

unique line postulate

Answer 13

through any two points there is only one line

Question 14

flat plane postulate

Answer 14

if two points are in a plane, then the line connecting those two is on the plane

Question 15

parallel postulate

Answer 15

Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Question 16

conditional statement

Answer 16

if p (hypothesis) then q (conclusion) (p –> q)

Question 17

converse

Answer 17

if q (conclusion) then p (hypothesis), symmetrical to conditional (q –> p)

Question 18

inverse

Answer 18

if not p (hypothesis), then not q (conclusion) (~p –> ~q)

Question 19

contrapositive

Answer 19

if not q (conclusion), then not p (hypothesis) (~q –> ~p)

Question 20

the only time a conditional statement is false

Answer 20

when p (hypothesis) true but q (conclusion) false

Question 21

the only time a converse is false

Answer 21

when p is false and q is true

Question 22

the only time an inverse is false

Answer 22

~p is true and ~q is false

Question 23

the only time a contrapositive is false

Answer 23

~p is false and ~q is true

Question 24

1. truth values for ___ and _____ are same

Answer 24

converse/conditional statement, inverse/contrapositive

Question 25

logically equivalent =

Answer 25

reverse p and q but dont reverse ~

Question 26

angle

Answer 26

two rays with a common endpoint

Question 26

rays

Answer 26

lines that go infinitely in one direction but not the other

Question 26

p ^ q

Answer 26

p and q (p is not hypothesis, neither is q)

Question 26

symmetric property

Answer 26

a = b –> b = a

Answer 26

and

Question 26

p v q

Answer 26

p or q (neither p or q is hypothesis) (the “or” is one or the other or both)

Question 27

compound statement

Answer 27

2 or more statements connected by “and” or “or”

Question 27

biconditional statement

Answer 27

can be written in the form (p if and only if q) or written in the form (if p then q, and if q then p)