Chapter 2

Question 0

Conjecture

Answer 0

A conclusion in a statement form.

Question 1

Inductive Reasoning

Answer 1

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

Question 2

Counter example

Answer 2

An example the disproves a conjectures

Question 3

Statement

Answer 3

A statement with a truth value

Question 4

Truth value

Answer 4

True or false

Question 5

Negation

Answer 5

Opposite symbol ~

Question 6

Compound statement

Answer 6

Two state joined together by an and or or

Question 7

Conjunction

Answer 7

AND compound statement

Question 8

Disconjuction

Answer 8

OR compound statement

Question 9

Truth table

Answer 9

A way to organize the truth values of your statements

Question 10

^ AND

Answer 10

2 or more have to be true

Question 11

or ⚓️

Answer 11

One or more has to be true

Question 12

Conditional

Answer 12

“If, then” statement

Question 13

Converse

Answer 13

If q, then p

Question 14

Inverse

Answer 14

If ~p, then ~q

Question 15

Contrapositive

Answer 15

If ~q, then ~p

Question 16

Biconditional

Answer 16

p if and only if q

Question 17

Inductive Reasoning

Answer 17

Make a conclusion based on past events and patterns

Question 18

Deductive Reasoning

Answer 18

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

Question 19

Law of detachment

Answer 19

Given: p->q

p

Question 20

Law of Syllogism

Answer 20

Given: p->q
q->r

Conclusion: p->r

Question 21

Postulate

Answer 21

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

Question 22

Theorem

Answer 22

Rule/law/statement - is proven/accepted

Question 23

Through any 2 points exactly 1 line can be drawn

Answer 23

Postulate 2.1

Question 24

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

Answer 24

Postulate 2.2

Question 25

A line contains at least 2 points

Answer 25

Postulate 2.3

Question 26

A plane contains at least 3 non collinear points

Answer 26

Postulate 2.4

Question 27

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

Answer 27

Postulate 2.5

Question 28

If two lines intersect then their intersection is a point

Answer 28

Postulate 2.6

Question 29

If two planes intersect then their intersection is a line

Answer 29

Postulate 2.7

Question 30

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

Answer 30

Midpoint of a line segment

Question 31

Proof

Answer 31

Supporting a conjecture through deductive reasoning

Question 32

Reflexive property

Answer 32

A=A

Question 33

Symmetric Property

Answer 33

If x=2 then 2=x

Question 34

Distributive property

Answer 34

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

Question 35

Transitive property

Answer 35

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

Question 35

Segment Addition Property

Answer 35

AC+CB=AB

Question 37

Complement theorem

Answer 37

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

Question 38

Congruent Supplements Theorem

Answer 38

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

Question 39

Congruent complements theorem

Answer 39

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

Question 40

Supplement theorem

Answer 40

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

Question 41

Vertical angles theorem

Answer 41

All vertical angles are congruent

Question 42

Perpendicular lines form 4 right angles

Answer 42

Right angle theorems

Question 43

All right angles are congruent

Answer 43

Right angle theorems

Question 44

Perpendicular lines form congruent adjacent angles

Answer 44

Right angle theorems

Question 45

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

Answer 45

Right angle theorems

Question 46

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

Answer 46

Right angle theorems

Question 47

Triangle Angle Sum Theorem

Answer 47

The 3 angles of any triangle add to 180

Question 48

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

Answer 48

Perpindicular bisector theorem

Question 49

Steps to indirect proofs

Answer 49

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

Question 50

The triangle inequality theorem

Answer 50

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

Question 51

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

Answer 51

Converse of the Hinge Theorem

Question 52

Sum of all angles of a convex polygon | 180(n-2)

Answer 52

Polygon interior angle sum

Question 53

360 degrees Each angle of a regular polygon 360/n

Answer 53

Polygon exterior angle sum

Question 54

Diagonals bisect eachother in a parallelogram

Answer 54

Theorem 6.7

Question 55

* 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

Answer 55

Tests for parallelograms

Question 56

Diagonals of a rectangle

Answer 56

Diagonals of a rectangle are congruent

Question 57

Rhombus has perpendicular diagonals

Answer 57

Theorem 6.15

Question 58

The diagonals of a rhombus bisect one pair of opposite angles

Answer 58

Theorem 6.16

Question 59

Rhombus has a pair of consecutive sides that are congruent

Answer 59

Theorem 6.19

Question 60

A square is a rhombus and a rectangle

Answer 60

Theorem 6.20

Question 61

Trapezoid

Answer 61

Quad. With one pair of parallel opposite sides

Question 62

An isosceles trapazoid has each pair of base angles being congruent

Answer 62

Theorem 6.21

Question 63

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

Answer 63

Theorem 6.23

Question 64

If a quad is a kite then the diagonals are congruent

Answer 64

Theorem 6.25

Question 65

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

Answer 65

Theorem 6.26