Chapter 2 Overview

Question 1

inductive reasoning

Answer 1

reasoning based on patterns you observe

Question 2

conjecture

Answer 2

conclusion you reach using inductive reasoning

Question 3

counterexample

Answer 3

an example that shows a conjecture is incorrect

Question 4

Conditional Statements

Answer 4

conditional → if-then statement
hypothesis → part p that follows if
conclusion → part q that follows then

(p → q ; read “If p, then q.”)

Question 5

negation

Answer 5

opposite of the statement

symbol is ~ p and read “not p”

Question 6

converse
(switch the
hypothesis &
conclusion)

Answer 6

If ∠ A is acute, then m ∠ A = 15.

(q → p)

Question 7

inverse
(negate both
hypothesis &
conclusion)

Answer 7

If m ∠ A ≠ 15, then ∠ A is not acute.

~ p → ~ q

Question 8

contrapositive
(negate both the
hypothesis & conclusion
of the converse)

Answer 8

If ∠ A is not acute, then m ∠ A ≠ 15.

~ q → ~ p

Question 9

Equivalent Statements

Answer 9

have the same truth value

A conditional and its contrapositive are equivalent statements. They are
both true or both false.

The converse and inverse are also equivalent statements.

Question 10

compound statement

Answer 10

combines 2 or more statements

Question 11

conjunction

Answer 11

Connect two or more
statements with and.

s ⋀ j
You say “s and j.”

A conjunction is true only when both statements are true.

Question 12

disjunction

Answer 12

Connect two or more
statements with or.

s ∨ j
You say “s or j.”

A disjunction is false only when both statements are false.

Question 13

truth table

Answer 13

lists all possible combinations of truth values for 2 or more statements

Question 14

biconditional

Answer 14

single true statement that combines a true conditional and its true converse

➢ uses the phrase “if and only if”

Question 15

Biconditional Statement

Answer 15

Combines p → q and q → p as p ↔ q

( read “p if and only if q”)

Question 16

deductive reasoning

Answer 16

process of reasoning logically from given statements or

facts to a conclusion

Question 17

Law of Detachment

Answer 17

Law
If the hypothesis of a true conditional is true,
the conclusion is true.

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

Question 18

Law of Syllogism

Answer 18

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

Symbols
If p → q is true
And q → r is true,
Then p → r is true.

Question 19

Theorem 2-1: Vertical Angles Theorem

Answer 19

Vertical Angles are congruent

Question 20

Theorem 2-2: Congruent Supplement Theorem

Answer 20

If two angles are supplements of the same angle (or of congruent angles), then the two
angles are congruent.

Question 21

Theorem 2-3 Congruent Complements Theorem:

Answer 21

If two angles are complements of the same angle (or of congruent angles), then the two
angles are congruent.

Question 22

Theorem 2-4

Answer 22

All right angles are congruent.

Question 23

Theorem 2-5

Answer 23

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