geometry midterm definitions

5.0(9)
studied byStudied by 347 people
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/204

flashcard set

Earn XP

Description and Tags

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

205 Terms

1
New cards

(1.2) undefined terms

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

2
New cards

(1.2) point

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

3
New cards

(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

4
New cards

(1.2) plane

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

5
New cards

(1.2) space

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

6
New cards

(1.2) collinear points

points all in ONE line

7
New cards

(1.2) coplanar points

points all in ONE plane

8
New cards

(1.2) intersection

the set of all points in both (all) figures

9
New cards

(1.3) between

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

10
New cards

(1.3) segment

2 points and all points BETWEEN them

11
New cards

(1.3) ray

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

12
New cards

(1.3) opposite rays

collinear rays that share EXACTLY ONE point

13
New cards

(1.3) postulates

statements that are accepted without proof

14
New cards

(1.3) segment addition postulate

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

15
New cards

(1.3) midpoint

point that divides a segment into two CONGRUENT segments

16
New cards

(1.3) congruent

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

17
New cards

(1.3) congruent segments

segments are congruent if and only if their measurements are EQUAL

18
New cards

(1.3) segment bisector

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

19
New cards

(1.4) angle

figure formed by two rays that have the endpoint

20
New cards

(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

21
New cards

(1.4) acute angle

angle whose measure is between 0 and 90

22
New cards

(1.4) right angle

angle whose measure is 90

23
New cards

(1.4) obtuse angle

angle whose measure is between 90 and 180

24
New cards

(1.4) straight angle

angle whose measure is 180

25
New cards

(1.4) protractor postulate

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

26
New cards

(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

27
New cards

(1.4) congruent angles

angles that have EQUAL measures

28
New cards

(1.4) adjacent angles

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

29
New cards

(1.4) linear pair

adjacent angles whose non-common sides form opposite rays

30
New cards

(1.4) angle bisector

the ray that divides and angle into CONGRUENT, adjacent angles

31
New cards

(1.5) 1. a line contains at least

  1. a plane contains at least __
  2. space contains at least
  1. 2 points
  2. 3 noncollinear points
  3. 4 non-coplanar points
32
New cards

(1.5) through any 2 points,

there is EXACTLY ONE line

33
New cards

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

  1. through any three noncollinear points, there is EXACTLY ONE _
  1. one plane
  2. plane
34
New cards

(1.5) if 2 points are in a plane,

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

35
New cards

(1.5) if 2 planes intersect,

then their intersection is a line

36
New cards

(1.5) if 2 lines intersect,

then they intersect in EXACTLY ONE point

37
New cards

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

there is EXACTLY ONE plane

38
New cards

(1.5) if 2 lines intersect,

then EXACTLY ONE plane contains the lines

39
New cards

(1.5) existence

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

40
New cards

(1.5) uniqueness

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

41
New cards

logic

study of methods and principles that allows you to classify arguments

42
New cards

(logic) simple statements

statements that are either true or false

43
New cards

(logic) compound statements

the joining of 2 or more simple statements

44
New cards

(logic) conjunction

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

45
New cards

(logic) disjunction

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

46
New cards

(logic) truth tables

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

47
New cards

(logic) inclusive "OR"

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

48
New cards

(logic) exclusive "OR"

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

49
New cards

(logic) negation

p: Mr. Mann loves football

~p: Mr. Mann does not love football

50
New cards

(logic) conditionals

if p, then q

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

expressed as p-> q

51
New cards

(logic) hypothesis

you study hard (p)

52
New cards

(logic) conclusion

you pass the test (q)

53
New cards

(logic) converse

q -> p

54
New cards

(logic) inverse

~p -> ~q

55
New cards

(logic) contrapositive

~q -> ~p

56
New cards

(logic) biconditional

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

expressed as: p

57
New cards

(logic) tautology

LAST column of truth table is ALL TRUE

58
New cards

(logic) contradiction

LAST column of truth table is ALL FALSE

59
New cards

(logic) infer

to conclude from the given information

60
New cards

(logic) modus ponens

the way that affirms by affirming

p -> q

p

therefore, q

61
New cards

(logic) modus tollens

p -> q

~q

therefore, ~p

62
New cards

(logic) simplification

p ^ q

therefore, p

63
New cards

(logic) disjunctive syllogism

p ⌄ q

~p

therefore, q

64
New cards

(logic) contrapositive rule

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

65
New cards

(logic) double negation

~(~p) logically equivalent to p

66
New cards

(logic) commutative rules

p ^ q LE to q ^ p

p ⌄ q LE to q ⌄ p

67
New cards

(logic) associative rules

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

(p ⌄ q) v r LE to p v (q v r)

68
New cards

(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)

69
New cards

(logic) DeMorgan's rules

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

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

70
New cards

(logic) venn diagram

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

71
New cards

(logic) logically equivalent statements

statements are either BOTH true or BOTH false

72
New cards

(2.2) properties of equality (POE)

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

73
New cards

(2.2) properties of congruence (POC)

reflexive, symmetric, transitive

74
New cards

(2.2) midpoint theorem

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

75
New cards

(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

76
New cards

(2.4) complementary angles

2 angles whose measures have the sum of 90

77
New cards

(2.4) supplementary angles

2 angles whose measures have the sum of 180

78
New cards

(2.4) vertical angles

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

79
New cards

(2.4) vertical angle theorem

"vertical angles are congruent"

80
New cards

(2.5) perpendicular lines

2 lines that intersect to form at least one RIGHT angle

81
New cards

(2.5) if 2 lines are perpendicular,

then they form congruent, adjacent angles

82
New cards

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

then the lines are perpendicular

83
New cards

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

then the angles are complementary

84
New cards

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

then the 2 angles are congruent

85
New cards

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

then the 2 angles are congruent

86
New cards

(3.1) parallel lines

coplanar lines that DO NOT intersect

87
New cards

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

non coplanar lines

88
New cards

(3.1) parallel planes

planes that DO NOT intersect

89
New cards

(3.1) line and a plane are parallel if:

they DO NOT intersect

90
New cards

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

then the lines of intersection are parallel

91
New cards

(3.1) transversal

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

92
New cards

(3.1) corresponding angles

2 angles in corresponding positions relative to the 2 lines

93
New cards

(3.1) alternate interior angles

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

94
New cards

(3.1) alternate exterior angles

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

95
New cards

(3.1) same side interior angles

2 interior angles on the same side of the transversal

96
New cards

(3.1) same side exterior angles

2 exterior angles on the same side of the transversal

97
New cards

(3.2) corresponding angle postulate

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

98
New cards

(3.2) alternate interior angle theorem

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

99
New cards

(3.2) same side interior angle theorem

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

100
New cards

(3.2) alternate exterior angle theorem

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