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Geometry > Chapter 2 > Flashcards

Chapter 2 Flashcards

0
Q

Conjecture

A

A conclusion in a statement form.

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1
Q

Inductive Reasoning

A

Forming a Conclusion based on examples, history of events, and/or patterns

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2
Q

Counter example

A

An example the disproves a conjectures

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3
Q

Statement

A

A statement with a truth value

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4
Q

Truth value

A

True or false

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5
Q

Negation

A

Opposite symbol ~

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6
Q

Compound statement

A

Two state joined together by an and or or

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7
Q

Conjunction

A

AND compound statement

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8
Q

Disconjuction

A

OR compound statement

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9
Q

Truth table

A

A way to organize the truth values of your statements

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10
Q

^ AND

A

2 or more have to be true

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11
Q

or ⚓️

A

One or more has to be true

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12
Q

Conditional

A

“If, then” statement

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13
Q

Converse

A

If q, then p

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14
Q

Inverse

A

If ~p, then ~q

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15
Q

Contrapositive

A

If ~q, then ~p

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16
Q

Biconditional

A

p if and only if q

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17
Q

Inductive Reasoning

A

Make a conclusion based on past events and patterns

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18
Q

Deductive Reasoning

A

Make a conclusion based on rules, laws, theorems, postulates, axiom, and definitions

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19
Q

Law of detachment

A

Given: p->q

p

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20
Q

Law of Syllogism

A

Given: p->q
q->r

Conclusion: p->r

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21
Q

Postulate

A

Rule/law/statement -accepted to be true (not proven)

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22
Q

Theorem

A

Rule/law/statement - is proven/accepted

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23
Q

Through any 2 points exactly 1 line can be drawn

A

Postulate 2.1

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24
Q

Through any non-collinear 3 pointy here is exactly 1 plane

A

Postulate 2.2

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25
Q

A line contains at least 2 points

A

Postulate 2.3

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26
Q

A plane contains at least 3 non collinear points

A

Postulate 2.4

27
Q

If 2 points lie in a plane then all the points that on the line connecting the points lie in the plane

A

Postulate 2.5

28
Q

If two lines intersect then their intersection is a point

A

Postulate 2.6

29
Q

If two planes intersect then their intersection is a line

A

Postulate 2.7

30
Q

If M is the midpoint of AB then AM is congruent to MB

A

Midpoint of a line segment

31
Q

Proof

A

Supporting a conjecture through deductive reasoning

32
Q

Reflexive property

A

A=A

33
Q

Symmetric Property

A

If x=2 then 2=x

34
Q

Distributive property

A

2(x+y)=2x+2y

35
Q

Transitive property

A

If x=y and y=z then x=z

35
Q

Segment Addition Property

A

AC+CB=AB

37
Q

Complement theorem

A

If the noncommon sides of two adjacent angles form a 90 degree angle then the angles are complementary

38
Q

Congruent Supplements Theorem

A

If two angles are supplementary to the same angle then these to original angles are equal to eachother

39
Q

Congruent complements theorem

A

If two angles are complementary to the same angle then those two angles are equal to eachother

40
Q

Supplement theorem

A

If 2 angles form a linear pair, they are supplementary angles

41
Q

Vertical angles theorem

A

All vertical angles are congruent

42
Q

Perpendicular lines form 4 right angles

A

Right angle theorems

43
Q

All right angles are congruent

A

Right angle theorems

44
Q

Perpendicular lines form congruent adjacent angles

A

Right angle theorems

45
Q

If 2 angles are congruent and supplementary then they are right angles

A

Right angle theorems

46
Q

If 2 congruent angles form a linear pair then they are right angles

A

Right angle theorems

47
Q

Triangle Angle Sum Theorem

A

The 3 angles of any triangle add to 180

48
Q

If a point is on the perpendicular bisector of a segment, then it is equidistant from the end point

A

Perpindicular bisector theorem

49
Q

Steps to indirect proofs

A

1) assume temporarily that the conclusion is false
2) reason logically (while giving reasons to support) until a contradiction is reached
3) contradiction has been met then temporary assumption is not valid and the conclusion must be true

50
Q

The triangle inequality theorem

A

The sum of any two sides of a triangle must be greater than the third side

51
Q

If two sides of a triangle are congruent to two sides of another triangle AND the third side of the 1st triangle is greater than the 3rd side of the 2nd triangle, then the angle of the 1st triangle is greater than the angle of the second triangle

A

Converse of the Hinge Theorem

52
Q

Sum of all angles of a convex polygon

180(n-2)

A

Polygon interior angle sum

53
Q

360 degrees
Each angle of a regular polygon
360/n

A

Polygon exterior angle sum

54
Q

Diagonals bisect eachother in a parallelogram

A

Theorem 6.7

55
Q
  • Both pair of opposite sides are congruent
  • both pairs of opposite angles are congruent
  • the diagonals bisect eachother
  • one pair of opposite sides is congruent and parallel
  • has both sides parallel
A

Tests for parallelograms

56
Q

Diagonals of a rectangle

A

Diagonals of a rectangle are congruent

57
Q

Rhombus has perpendicular diagonals

A

Theorem 6.15

58
Q

The diagonals of a rhombus bisect one pair of opposite angles

A

Theorem 6.16

59
Q

Rhombus has a pair of consecutive sides that are congruent

A

Theorem 6.19

60
Q

A square is a rhombus and a rectangle

A

Theorem 6.20

61
Q

Trapezoid

A

Quad. With one pair of parallel opposite sides

62
Q

An isosceles trapazoid has each pair of base angles being congruent

A

Theorem 6.21

63
Q

If and only if a trapezoid is isosceles then it has congruent diagonals

A

Theorem 6.23

64
Q

If a quad is a kite then the diagonals are congruent

A

Theorem 6.25

65
Q

If a quad is a kite then exactly one pair of opposite angles are congruent

A

Theorem 6.26

Geometry (5 decks)

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