Geometry Chapter 14

Question 1

The inverse of a true statement

Answer 1

is not necessarily true.

Question 2

All terms in a definition

Answer 2

must have been previously defined (or be those that, by agreement, are left undefined).

Question 2

Partial converse of a theorem

Answer 2

is formed by interchanging any one condition in the hypothesis with one consequence in the conclusion.

Question 2

If a statement is false and its converse is true

Answer 2

then the conditions in the hypothesis are necessary but not sufficient for its conclusion.

Question 2

If a statement and its converse are both false

Answer 2

then the conditions in the hypothesis are neither necessary nor sufficient for its conclusion

Question 3

The inverse of a statement is formed

Answer 3

by denying both the hypothesis and the conclusion

Question 4

The contrapositive of a false statement

Answer 4

is false.

Question 5

Statements that are not logically equivalent are

Answer 5

a) a statement and its inverse
b) a statement and its converse
c) the converse and the contrapositive of the same statement.
d) the inverse and the contrapositive of the same statement

Question 7

The distinguishing characteristics of a defined term

Answer 7

should be as few as possible.

Question 8

If a statement is true and its converse is false

Answer 8

then the conditions in the hypothesis of the statement are sufficient but not necessary for its conclusion.

Question 9

The converse of a statement

Answer 9

is the statement that is formed by interchanging the hypothesis and the conclusion

Question 10

Undefined terms:

Answer 10

Point, line, and surface

Question 10

The negative of a statement

Answer 10

is the denial of the statement

Question 11

The term being defined should be distinguished

Answer 11

from all other members of its class.

Question 11

The converse of a true statement other than a definition

Answer 11

is not necessarily true.

Question 13

The term being defined

Answer 13

should be placed in the next larger set or class to which it belongs.

Question 14

The contrapositive of a statement is formed by

Answer 14

interchanging the negative of the hypothesis with a negative of the conclusion. Hence the contrapositive is the converse of the inverse and the inverse of the converse.

Question 15

Logically equivalent pairs of statements are

Answer 15

a) A statement and its contrapositive
b) the inverse and the converse of the same statement.

Question 17

A statement is considered false if

Answer 17

one false instance of the statement exists.

Question 20

Partial Inverse of a theorem

Answer 20

formed by denying one condition in the hypothesis and one consequence in the conclusion.

Question 21

The converse of a definition is

Answer 21

true

Question 22

If a statement and its converse are both true

Answer 22

then the conditions in the hypothesis of the statement are necessary and sufficient for its conclusion

Question 23

The contrapositive of a true statement

Answer 23

is true

Question 24

Logically equivalent statements are

Answer 24

pairs of related statements that are either both true or both false.