Chapter 2

Question 1

what is a conditional statement?

Answer 1

a logical statement that has a hypothesis and conclusion.

Question 2

what form is a conditional statement written in?

Answer 2

if-then form

Question 3

what is a converse statement?

Answer 3

a statement that exchanges the hypothesis and conclusion.

Question 4

what is the form for a converse statement?

Answer 4

q–>p

Question 5

what is the form for a conditional statement?

Answer 5

p–>q

Question 6

what is an inverse statement?

Answer 6

when you negate both the hypothesis and conclusion

Question 7

what is the form for a converse statement?

Answer 7

q –> p

Question 8

what is a contrapositive statement?

Answer 8

a converse statement with negation

Question 9

what is the form for a contrapositive statement?

Answer 9

-q–>-p

Question 10

if the original is true, what happens to the contrapositive statement?

Answer 10

it’s true

Question 11

if the original is false, what happens to the contrapositive statement?

Answer 11

it’s false

Question 12

what are perpendicular lines?

Answer 12

two lines that form a right angle when they intersect.

Question 13

what is a biconditional statement?

Answer 13

when a conditional & converse statement are both true.

Question 14

what is the form for biconditional statements?

Answer 14

p < — > q

Question 15

what is a conjecture?

Answer 15

an unproven statement that is based on observation.

Question 16

what is inductive reasoning?

Answer 16

the process of finding a pattern for specific cases and then writing a conjecture for the general case.

Question 17

what is a counterexample?

Answer 17

a statement to show the conjecture is false.

Question 18

what does nonzero mean?

Answer 18

you can’t use zeros.

Question 19

what is deductive reasoning?

Answer 19

when you use facts and laws of logic to form a logical argument.

Question 20

what does the law of detachment say?

Answer 20

if the following two statements are true. Then we can derive a third true statement

Question 21

what does the law of syllogism say?

Answer 21

if p, then q
if q, then r
therefore: if p, then r

Question 22

to use the law of syllogism what must you do?

Answer 22

use the hypothesis in one statement and the conclusion in another

Question 23

what does the addition property say?

Answer 23

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

Question 24

what does the subtraction property say?

Answer 24

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

Question 25

what does the multiplication property say?

Answer 25

if a=b, then ac = bc

Question 26

what does the division property say?

Answer 26

if a=b, then a/c = b/c

Question 27

what does the distributive property say?

Answer 27

a(b+c) = ab +ac

Question 28

what does the substitution property say?

Answer 28

if a=b, then a can be substituted for b in any equation.

Question 29

what does the reflexive property say?

Answer 29

a=a

Question 30

what does the symmetric property say?

Answer 30

if a=b, then b=a

Question 31

what does the transitive property say?

Answer 31

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

Question 32

what is theorem 2.4?

Answer 32

congruent supplements theorem

Question 33

what does the congruent supplements theorem say?

Answer 33

if two angles are supplementary to the same angle, then they are congruent.

Question 34

what is theorem 2.5?

Answer 34

congruent complements theorem

Question 35

what does the congruent complements theorem say?

Answer 35

if two angles are complementary to the same angle, then they are congruent.

Question 36

what is theorem 2.6?

Answer 36

vertical angles congruence theorem

Question 37

what does the vertical angles congruence theorem say?

Answer 37

vertical angles are congruent.