Studied by 39 people

5.0(3)

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Hint

1

(1.2) undefined terms

intuitive ideas, basis of ALL geometry (point, line, and plane)

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2

(1.2) point

undefined; a location is space that has no thickness, all figures are made up of points

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3

(1.2) line

undefined; extends in opposite directions without ending and has no thickness and cannot be measured. made up of infinite number of points

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4

(1.2) plane

undefined; a flat surface that goes on forever and has no thickness

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5

(1.2) space

the set of ALL points, represented by 4 non-coplanar points

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6

(1.2) collinear points

points all in ONE line

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(1.2) coplanar points

points all in ONE plane

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8

(1.2) intersection

the set of all points in both (all) figures

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9

(1.3) between

for N to be "between" M and P, all 3 points must be collinear and N must be in the middle

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10

(1.3) segment

2 points and all points BETWEEN them

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(1.3) ray

segment XY and all points Z, such that Y is between X and Z

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12

(1.3) opposite rays

collinear rays that share EXACTLY ONE point

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13

(1.3) postulates

statements that are accepted without proof

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14

(1.3) segment addition postulate

if B is between A and C, then AB + BC = AC

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15

(1.3) midpoint

point that divides a segment into two CONGRUENT segments

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(1.3) congruent

objects (or figures) that have the same EXACT size and shape

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17

(1.3) congruent segments

segments are congruent if and only if their measurements are EQUAL

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18

(1.3) segment bisector

a line, segment, ray, or plane that intersects a segment at its midpoint

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19

(1.4) angle

figure formed by two rays that have the endpoint

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20

(1.4) point on interior

a point is on the interior of an angle if and only if it lies on a segment whose endpoints are on the angle, but the point is not

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21

(1.4) acute angle

angle whose measure is between 0 and 90

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22

(1.4) right angle

angle whose measure is 90

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23

(1.4) obtuse angle

angle whose measure is between 90 and 180

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24

(1.4) straight angle

angle whose measure is 180

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25

(1.4) protractor postulate

(NOT WORD FOR WORD) says that every straight line is 180

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26

(1.4) angle addition postulate

if point K lines in the interior of angle JGH, the the measure of angle JGK + the measure of angle KGH = the measure of angle JGH

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(1.4) congruent angles

angles that have EQUAL measures

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28

(1.4) adjacent angles

TWO angles IN A PLANE that have a common vertex and a common side but no common interior points

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(1.4) linear pair

adjacent angles whose non-common sides form opposite rays

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(1.4) angle bisector

the ray that divides and angle into CONGRUENT, adjacent angles

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31

(1.5) 1. a line contains at least ________

a plane contains at least __________

space contains at least ______________

2 points

3 noncollinear points

4 non-coplanar points

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(1.5) through any 2 points,

there is EXACTLY ONE line

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(1.5) 1. through any three points, there is at least _________

through any three noncollinear points, there is EXACTLY ONE _____

one plane

plane

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34

(1.5) if 2 points are in a plane,

then the line that contains the points, is in that plane

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(1.5) if 2 planes intersect,

then their intersection is a line

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(1.5) if 2 lines intersect,

then they intersect in EXACTLY ONE point

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(1.5) through a line and a point not on that line,

there is EXACTLY ONE plane

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38

(1.5) if 2 lines intersect,

then EXACTLY ONE plane contains the lines

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(1.5) existence

"at least one"; the situation exists, however there could be more than one example

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40

(1.5) uniqueness

"exactly one"; there is only one example that satisfies a given condition

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41

logic

study of methods and principles that allows you to classify arguments

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42

(logic) simple statements

statements that are either true or false

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43

(logic) compound statements

the joining of 2 or more simple statements

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44

(logic) conjunction

p ^ q; the joining of 2 simple statements with the word "and"

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45

(logic) disjunction

p ⌄ q; joining of 2 simple statements with the word "or"

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46

(logic) truth tables

used to tell under what conditions a compound statement is true or false

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47

(logic) inclusive "OR"

TRUE if the first, second, or both statements are true (USED IN OUR CLASS)

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48

(logic) exclusive "OR"

implies that the first or second statement are true, but not both

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49

(logic) negation

p: Mr. Mann loves football

~p: Mr. Mann does not love football

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50

(logic) conditionals

if p, then q

ex. if you study hard, then you pass the test

expressed as p-> q

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(logic) hypothesis

you study hard (p)

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(logic) conclusion

you pass the test (q)

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(logic) converse

q -> p

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(logic) inverse

~p -> ~q

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(logic) contrapositive

~q -> ~p

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(logic) biconditional

(iff) can be used if the conditional and converse are both true

expressed as: p <-> q

expressed as: p <-> q

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(logic) tautology

LAST column of truth table is ALL TRUE

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58

(logic) contradiction

LAST column of truth table is ALL FALSE

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59

(logic) infer

to conclude from the given information

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60

(logic) modus ponens

the way that affirms by affirming

p -> q

p

therefore, q

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61

(logic) modus tollens

p -> q

~q

therefore, ~p

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62

(logic) simplification

p ^ q

therefore, p

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(logic) disjunctive syllogism

p ⌄ q

~p

therefore, q

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(logic) contrapositive rule

p -> q logically equivalent to ~q -> ~p

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65

(logic) double negation

~(~p) logically equivalent to p

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66

(logic) commutative rules

p ^ q LE to q ^ p

p ⌄ q LE to q ⌄ p

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67

(logic) associative rules

(p ^ q) ^ r LE to p ^ (q ^ r)

(p ⌄ q) v r LE to p v (q v r)

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(logic) distributive rules

p ^ ( q ^ r) LE to (p ^ q) v (p ^ r)

p v (q ^ r) LE to (p v q) ^ (p v r)

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69

(logic) DeMorgan's rules

~ (p ^ q) LE to ~p v ~q

~ (p v q) LE to ~p ^ ~q

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(logic) venn diagram

picture that shows logical relationships between sets of data, used to determine whether an argument leads to a valid conclusion

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(logic) logically equivalent statements

statements are either BOTH true or BOTH false

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(2.2) properties of equality (POE)

addition, subtraction, multiplication, division, substitution, reflexive, symmetric, transitive

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(2.2) properties of congruence (POC)

reflexive, symmetric, transitive

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74

(2.2) midpoint theorem

if M is the midpoint of segment AB, then AM = 1/2 AB and MB = 1/2 AB

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75

(2.2) angle bisector theorem

if ray BX is the bisector of angle ABC, then measure of angle ABX = 1/2 measure of angle ABC and measure of angle XBC = 1/2 measure of ABC

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(2.4) complementary angles

2 angles whose measures have the sum of 90

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(2.4) supplementary angles

2 angles whose measures have the sum of 180

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(2.4) vertical angles

2 angles such that the sides of one angle are opposite rays to the sides of the other angle

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(2.4) vertical angle theorem

"vertical angles are congruent"

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(2.5) perpendicular lines

2 lines that intersect to form at least one RIGHT angle

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(2.5) if 2 lines are perpendicular,

then they form congruent, adjacent angles

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82

(2.5) if 2 lines form congruent, adjacent angles,

then the lines are perpendicular

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83

(2.5) if the exterior sides of adjacent, acute angles are perpendicular,

then the angles are complementary

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84

(2.6) if 2 angles are supplements of congruent angles (or the same angle),

then the 2 angles are congruent

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85

(2.6) if 2 angles are complements of congruent angles (or the same angle),

then the 2 angles are congruent

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86

(3.1) parallel lines

coplanar lines that DO NOT intersect

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87

(3.1) skew lines (can be segments and rays too)

non coplanar lines

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88

(3.1) parallel planes

planes that DO NOT intersect

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89

(3.1) line and a plane are parallel if:

they DO NOT intersect

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90

(3.1) if 2 parallel planes are cut by a third plane,

then the lines of intersection are parallel

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91

(3.1) transversal

a line that intersects two or more coplanar lines in different points

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(3.1) corresponding angles

2 angles in corresponding positions relative to the 2 lines

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(3.1) alternate interior angles

2 non-adjacent interior angles on opposite sides of the transversal

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94

(3.1) alternate exterior angles

2 non-adjacent exterior angles on opposite sides of the transversal

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95

(3.1) same side interior angles

2 interior angles on the same side of the transversal

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(3.1) same side exterior angles

2 exterior angles on the same side of the transversal

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(3.2) corresponding angle postulate

if 2 parallel lines are cut by a transversal, then corresponding angles are congruent

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98

(3.2) alternate interior angle theorem

if 2 parallel lines are cut by a transversal, then alternate interior angles are congruent

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99

(3.2) same side interior angle theorem

if 2 parallel lines are cut by a transversal, then same side interior angles are supplementary

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(3.2) alternate exterior angle theorem

if 2 parallel lines are cut by a transversal, then alternate exterior angles are congruent

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