Geometry Jacobs 3E Ch 02

Front 1

conditional statement

Back 1

A statement containing two clauses, one that begins with “if” or “when” or an equivalent word; and one that can begin with “then”.

Front 2

a --> b

Back 2

Symbolic representation of a conditional statement.

Front 3

If a, then b.

Back 3

a --> b

Front 4

Euler diagram

Back 4

Circle diagrams that can represent conditional statements.

Front 5

Converse of a --> b

Back 5

b --> a

Front 6

Inverse of a --> b

Back 6

not a --> not b
or
~a --> ~b

Front 7

Contrapositive of a --> b

Back 7

not b --> not a
or
~b --> ~a

Front 8

When a statement and its converse are true, we can write…

Back 8

a if and only if b
or
a iff b

Front 9

syllogism

Back 9

An argument in the form of

a --> b

b --> c
Therefore a --> c

Front 10

direct proof

Back 10

a --> b

b --> c

…

m -->n

Therefore a --> n

Front 11

premises

Back 11

Statements in the form

a --> b
b --> c

that build an argument.

Front 12

conclusion

Back 12

a --> n

Front 13

If all of the premises of an argument are true and the logic of the argument is correct, then...

Back 13

...the conclusion must be true.

Front 14

indirect proof

Back 14

A form of proof which is begun with an assumption opposite to the desired conclusion. The logical argument that follows leads to a contradiction, which then proves the desired conclusion.

Front 15

postulate

Back 15

A statement that is assumed to be true without proof.

Front 16

theorem

Back 16

A statement that is proved by reasoning deductively.

Front 17

Postulate 1

Back 17

Two points determine a line.

Front 18

Postulate 2

Back 18

Three noncollinear points determine a plane.

Front 19

Pythagorean Theorem

Back 19

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Front 20

The sum of the angles of a triangle is 180°.

Back 20

The triangle angle sum theorem.

Front 21

Formula for the circumference of a circle.

Back 21

Circumference = pi • d.

Front 22

Formula for the area of the circle.

Back 22

Area = pi • (square of radius)

Front 23

A statement containing two clauses, one that begins with “if” or “when” or an equivalent word; and one that can begin with “then”.

Back 23

Conditional statement.

Front 24

Symbolic representation of a conditional statement.

Back 24

a --> b

Front 25

An argument in the form of

a --> b

b --> c
Therefore a --> c

Back 25

syllogism

Front 26

a --> b

b --> c

…

m -->n

Therefore a --> n

Back 26

direct proof

Front 27

Area = pi • (square of radius)

Back 27

Formula for the area of a circle.

Front 28

Circumference = pi • d.

Back 28

Formula for the circumference of a circle.

Front 29

The triangle angle sum theorem.

Back 29

The sum of the angles in a triangle is 180°.

Front 30

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Back 30

Pythagorean theorem.

Front 31

Three noncollinear points determine a plane.

Back 31

Postulate 2.

Front 32

Two points determine a line.

Back 32

Postulate 1.

Front 33

A statement that is proved by reasoning deductively.

Back 33

theorem

Front 34

A statement that is assumed to be true without proof.

Back 34

postulate