Math; Geometry; Ph: 08 - Ch 2

Front 1

"Conditional" statement

Back 1

"if-then" statement
if xxxxx, then yyyy
if "hypothesis", then "conclusion.

Front 2

Q: Truth value of conditional statement

Back 2

True -- everytime the hypothesis is true, then the conclusion is also true.
False - show that ONLY ONE counter-example showing hypothesis true and conclusion is false

Front 3

Q: Hypothesis and Conclusion within a conditional statement.

Back 3

Hypothesis is the "if" part;
Conclusion is the "then" part.

Front 4

Converse of a Conditional statement

Back 4

Reverse the if, then parts.
conditional: if xxx, then yyy.
converse: if yyy, then xxx.

Front 5

Biconditional statement.

Back 5

The statement you get by connecting the conditional and it's converse with "and".

The "converse" IF AND ONLY IF the "conditional"

Front 6

Deductive (logical) reasoning

Back 6

The process of reasoning logically from given statements to reach a conclusion.

Front 7

Law of Detachment

Back 7

If a conditional is true and it's hypothesis is true, then it's conclusion is true.

Front 8

(2-3)
Law of Syllogism

Back 8

If p, then q AND if q, then r are true
THEN
if p, then r is also true.
(2-3)

Front 9

(2-3)Symbolic way of writing a conditional statement

Back 9

p --> q.
means; if p , then q.

Front 10

(2-3)
Q: Description of Law of Syllogism

Back 10

allows you to state a conclusion from --
- two true conditional statements, when the conclusion of one statement is the hypothesis of the other

Front 11

(2-3)
Q: What types of statements make up the law of syllogism

Back 11

two conditional statements:

conditional (p --> q)
conditional (q --> r)

Front 12

Q: write the law of syllogsm (2-3) given:
if a number is prime, then it does not have repeated factors.
if a number does not have repeated factors, then it is not a perfect square.

Back 12

p - number is prime
q - does not have repeated factors
r -- is not a perfect square.
if a number is prime, then it is not a perfect square

Front 13

(2-4)
Addition property

Back 13

if a=b, then a+c = b+c

Front 14

(2-4)
Subtraction property

Back 14

if a=b, then a-c = a-b

Front 15

2-4
multiplication property

Back 15

if a=b, then a*b = b*c

Front 16

(2-4)
division property

Back 16

if a=b and c NE 0, then a/c - b/c

Front 17

(2-4)
reflexive property

Back 17

a=a

Front 18

(2-4) Symmetric property

Back 18

if a=b, then b=a

Front 19

(2-4) Transitive property

Back 19

if a=b and b=c, then a=c

Front 20

(2-4) substitution property

Back 20

if a=b, then b can replace a in any expression

Front 21

(2-4) distributive property

Back 21

a (b+c) = ab + ac

41 = 40+1
3(41) = 3(40) + 3(1).

Front 22

(2-4 distributive property

Back 22

ab + ac = a(b+c)
a is distributed across b & c.

Front 23

(2-1) angle addition postulate

Back 23

the sum of the small angles making a large angle = the large angle.

Front 24

(2-1) angle bisector

Back 24

A line bisecting (i.e. cutting in half) an angle results in two equal angles whos sum equals the original angle.

Front 25

(2-1) segment addition postulate

Back 25

the sum of the small segments making a large segment = the large segment.

Front 26

(2-4) reflexive property

Back 26

line ab CG to line ab
angle a CG to angel a

Front 27

(2-4) symmetric property

Back 27

if line ab CG to cd, then cd is CG to ab.
if angle a CG to angle B, then angle B CG angle A

Front 28

2-5
q: paragraph proof

Back 28

a proof written as sentences in a paragraph.

Front 29

2-5
q: theorem

Back 29

the statement that you prove, via a set of steps

Front 30

2-5
q:proof

Back 30

a series of steps , using deductive reasoning.

Front 31

2-5
q: postulate

Back 31

a proposition that is accepted as true in order to provide a basis for logical reasoning
(A self-evident or universally recognized truth)

Front 32

2-5
q: what are the steps in making a proof.

Back 32

1) list everything that is given.
2) list what you must show (prove).
3) list the steps (assumptions, postulates) to get to the proof).

Front 33

2-5
q: What is the vertical angles theorem?

Back 33

Vertical angles are congruent.

Front 34

2-5:
q: prove that vertical angles are congruent.

Back 34

given:
L1 and L2 are vertical angels
prove:
L1 = L2
steps
L1 +L3 = 180 angle addition p
L2 +L3 = 180 angle addition p
L1 +L3 = L2+L3 -subs
L1 = L2 sub L3 both sides

Front 35

2-5
q: if 2 angles are supplements of the same angle (or of congruent angles), then the 2 angles are congruent.

Back 35

given:
L1 and L2 are suppl.
L3 and L2 are suppl
prove:
L1 = L3
steps:
L1 + L2 = 180 defn suppl
L2 + L3 = 180 defn supp
L1 + L2 = L2+L3 subst
L1 + L3 subtr L2

Front 36

q:
2-5 how is a theorem different than a postulate

Back 36

A postulate is assumed true.
A theorem is proven true by steps based on deductive reasoning.

Front 37

q:
is this a good definition? why not.
A pencil is a writing instrument

Back 37

Conditional
if a pencil is an instrument than it is for writing.
Converse:
if it is used for writing it is an instrument.

Front 38

q: what makes a "good" definition - 3 items

Back 38

1) uses clearly understood or defined terms.
2) precise (not large, sort of, almost..).
3) reversible -- can write it as a biconditional.
4) no counter-examples.

Front 39

q: what is meant by reversible

Back 39

can be written as a true biconditional.

the conditional and the converse are true. p if and only if q.

Front 40

q: write the statements that form the biconditonal for:
two angles are congruent if and only if they have the same measure

Back 40

if two angles are congruent, then they have the same measure.

if two angles have the same measure than they are congruent.

Front 41

q: is this a good definition - why / why not.
A cat is an animal with whiskers.

Back 41

NO.
A counterexample is a dog which has whiskers.
if an animal is a cat than it has whiskers.
if an animal has whiskers it is a cat.