Chapter 2 Review

Question 1

inductive reasoning

Answer 1

reasoning that uses a number of specific examples to arrive at a conclusion

Question 2

conjecture

Answer 2

a concluding statement reached using inductive reasoning

Question 3

counterexample

Answer 3

the opposite of an example; a false example

Question 4

statement

Answer 4

a sentence that is either true or false, but not both

represented using a letter such as p or q

EX. p: A rectangle is a quadrilateral.

Question 5

truth value

Answer 5

the truth (T) or falsity (F) of a statement

EX. p: A rectangle is a quadrilateral. (Truth value: T)

Question 6

negation

Answer 6

a statement that has the opposite meaning and truth value of an original statment

not p is written _~p

Question 7

compound statment

Answer 7

two or more statments joined by teh word and or or

Question 8

conjunction

Answer 8

a compound statement using the word and

p and q is written p^q

*conjunctions are true ONLY if both statements are true

Question 9

disjunction

Answer 9

a compound statment that uses the word or

p or q is written p ν q

Question 10

truth table

Answer 10

a table used as a convenient method for organizing the truth values of statements

Question 11

conditional statement

Answer 11

a statement that can be written in if-then form

EX. If mthen

Question 12

if-then statement

Answer 12

if p then q is written p → q

Question 13

hypothesis

Answer 13

the phrase immediately following the word if

represnted by p

Question 14

conclusion

Answer 14

the phrase immediately following the word then

represented by q

Question 15

related conditionals

Answer 15

statements that are based on a given conditional statement

p→q

Question 16

converse

Answer 16

the statement formed by exchanging the hypothesis and conclusion of a conditional statement

p →q

EX. If

Question 17

inverse

Answer 17

the statement formed by negating both the hypothesis and conclusion of the conditional

_~p → _~q

EX. if mnot 35, then not an acute angle.

Question 18

contrapositive

Answer 18

the statment formed by negating both the hypothesis and the conclusion of the converse of the conditional

_~q → _~p

EX. If not an acute angle, then mnot 35.

Question 19

logically equivalent

Answer 19

statements with the same truth values

EX. A conditional statement and its contrapositive are logically equivalent.

The converse and inverse of a conditional are logically equivalent.

Question 20

deductive reasoning

Answer 20

Uses facts, rules, definitions, or properties to reach logical conclusions from given statements

Question 21

Law of Detachment

Answer 21

If p → q is a true statement and p is true, then q is true.

EX.

Given:If a car is out of gas, then it will not start. Sarah’s car is out of gas.

Valid conclusion: Sarah’s car will not start.

Question 22

Law of Syllogism

Answer 22

If p → q and q → r are true statements, then p → r is a true statement.

EX.

Given: If you get a job, then you will earn money. If you earn money, then you will buy a car.

Valid Conclusion: If you get a job, then you will buy a car.

Question 23

postulate / axiom

Answer 23

a statement that is accepted as true without proof

Question 24

Points and Lines Postulate 2.1

Answer 24

Through any two points, there is exactly one line

EX. Only one line goes through points A and B.

Question 25

Ponits and Planes Postulate 2.2

Answer 25

Through any three noncollinear points, there is exactly one plane. EX. Plane M is the only plane through noncollinear points A, B, and C

Question 26

Points and Lines Postulate 2.3

Answer 26

A line contains at least two points. Ex. The line contains points A and B.

Question 27

Points and Planes Postulate 2.4

Answer 27

A plane contains at least three noncollinear points. EX. Plane M contains points A, B, and C.

Question 28

Points, Lines, and Planes Postulate 2.5

Answer 28

If two points lie in a plane, then the entire line containing those points lies in that plane. EX. Points K and L are on the same plane.

Question 29

Intersections of Lines Postulate 2.6

Answer 29

If two lines intersect, then their intersection is exactly one point. EX. Lines l and m intersect at point A.

Question 30

Intersections of Planes Postulate 2.7

Answer 30

If two planes intersect, then their intersection is a line. EX. Planes *F* and *G* intersect in line *w*.

Question 31

proof

Answer 31

a logical argument in which each statement is supported by a statement that is accepted as true

Question 32

theorem

Answer 32

a statement of conjecture that has been proven

Question 33

paragraph proof or informal proof

Answer 33

a paragraph used to explain why a conjecture for a given situation is true

Question 34

two-column proof or formal proof

Answer 34

Proof that contains statements and reasons organized in two columns. Each step is called a statement, and the properties that justify each step are called reasons.

Question 35

Theorem 2.1: Midpoint Theorem

Answer 35

If M is the midpoint of AB, then AM ≅ BM

Question 36

algebraic proof

Answer 36

a proof that is made up of a series of algebraic statements

Question 37

Addition Property of Equality

Answer 37

If a = b, then a + c = b + c.

Question 38

Subtraction Property of Equality

Answer 38

If a = b, then a - c = b - c.

Question 39

Multiplication Property of Equality

Answer 39

If a = b, then a • c = b • c.

Question 40

Division Property of Equality

Answer 40

If a = b and c ≠ 0, then ^a/_C = ^b/_C.

Question 41

Reflexive Property of Equality

Answer 41

a = a

Question 42

Symmetric Property of Equality

Answer 42

If a = b, then b = a.

Question 43

Transitive Property of Equality

Answer 43

If a = b and b = c, then a = c.

Question 44

Substitution Property of Equality

Answer 44

If a = b, then *a* may be replaced by *b* in any equation or expression.

Question 45

Distributive Property

Answer 45

a(b+c) = ab + ac

Question 46

Reflexive Property of Congruence (with Segments)

Answer 46

AB ≅ AB

Question 47

Symmetric Property of Congruence (with Segments)

Answer 47

If AB ≅ CD, then CD ≅ AB

Question 48

Transitive Property of Congruence (with Segments)

Answer 48

If AB ≅ CD and CD ≅ EF, then AB ≅ EF

Question 49

Postulate 2.11 Angle Addition Postulate

Answer 49

C is the interior of ∠BAD if and only if m∠BAC + m∠CAD = m∠BAD

Question 50

Theorem 2.3: Supplement Theorem

Answer 50

If two angles form a linear pair, then they are supplementary angles. m∠1 + m∠2 = 180°

Question 51

Theorem 2.4: Complement Theorem

Answer 51

If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. m∠1 + m∠2 = 180

Question 52

Reflexive Property of Congruence (with Angles)

Answer 52

∠1 ≅ ∠1

Question 53

Symmetric Property of Congruence (with Angles)

Answer 53

If ∠1 ≅ ∠2, then ∠2 ≅ ∠1.

Question 54

Transitive Property of Congruence (with Angles)

Answer 54

If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.

Question 55

Theorem 2.6: Congruent Supplements Theorem

Answer 55

Angles supplementary to the same angle or to congruent angles are congruent.

Question 56

Theorem 2.7: Congruent Complements Theorem

Answer 56

Angles complementary to the same angle or to congruent angles are congruent.

Question 57

Theorem 2.8: Vertical Angles Theorem

Answer 57

If two angles are vertical angles, then they are congruent. EX. ∠1 ≅ ∠3 and ∠2 ≅ ∠4

Question 58

Right Angle Theorem 2.9

Answer 58

Perpendicular lines intersect to form four right angles.

Question 59

Right Angle Theorem 2.10

Answer 59

All right angles are congruent. EX. If ∠1, ∠2, ∠3, and ∠4 are ∟, then ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4

Question 60

Right Angle Theorem 2.11

Answer 60

Perpendicular lines form congruent adjacent angles. EX: If line a is perpendicular to line b, then ∠1 ≅ ∠2, ∠2 ≅ ∠4, ∠3 ≅ ∠4 and ∠1 ≅ ∠3

Question 61

Right Angle Theorem 2.12

Answer 61

If two angles are congruent and supplementary, then each angle is a right angle.

Question 62

Right Angle Theorem 2.13

Answer 62

If two congruent angles form a linear pair, then they are right angles.