Geometry Jacobs 3E Ch 05

Front 1

Three Possibilities Property

Back 1

When considering two quantities (line segments, angles…), one of these is true:
a = b
a < b
a > b

Front 2

Transitive Property of Inequality

Back 2

If a > b
and b > c
then a > c
(Works for < also.)

Front 3

Addition Property of Inequality

Back 3

If a > b
then
a + c > b + c.

Front 4

Subtraction Property of Inequality

Back 4

If a > b
then
a - c > b - c

Front 5

Multiplication Property of Inequality

Back 5

If a > b and c > 0
then ac > bc.
(If c < 0 then multiplying both sides by a negative would reverse the sense of the inequality.)

Front 6

Division Property of Inequality

Back 6

If a > b and c > 0
then
a ÷ c > b ÷ c.
(If c < 0 then multiplying both sides by a negative would reverse the sense of the inequality.)

Front 7

Addition Theorem of Inequality

Back 7

If a > b and c > d
then
a + c > b + d.

Front 8

Whole Greater than Part Theorem

Back 8

If a > 0, b > 0,
and a + b = c
then c > a
and c > b.

Front 9

Definition: An exterior angle of a triangle...

Back 9

is an angle that forms a linear pair with an angle of the triangle.

Front 10

Exterior Angle Theorem: An exterior angle of a triangle is...

Back 10

greater than either remote interior angle.

Front 11

Thm. If two sides of a triangle are unequal...

Back 11

the angles opposite them are unequal in the same order.

Front 12

Triangle Inequality Theorem

Back 12

The sum of any two sides of a triangle is greater than the third side.

Front 13

When considering two quantities (line segments, angles…), one of these is true:
a = b
a < b
a > b

Back 13

Three Possibilities Property

Front 14

If a > b
and b > c
then a > c
(Works for < also.)

Back 14

Transitive Property of Inequality

Front 15

If a > b
then
a + c > b + c.

Back 15

Addition Property of Inequality

Front 16

If a > b
then
a - c > b - c

Back 16

Subtraction Property of Inequality

Front 17

If a > b and c > 0
then ac > bc.
(If c < 0 then multiplying both sides by a negative would reverse the sense of the inequality.)

Back 17

Multiplication Property of Inequality

Front 18

If a > b and c > 0
then
a ÷ c > b ÷ c.
(If c < 0 then multiplying both sides by a negative would reverse the sense of the inequality.)

Back 18

Division Property of Inequality

Front 19

If a > b and c > d
then
a + c > b + d.

Back 19

Addition Theorem of Inequality

Front 20

If a > 0, b > 0,
and a + b = c
then c > a
and c > b.

Back 20

Whole Greater than Part Theorem

Front 21

greater than either remote interior angle.

Back 21

Definition: An exterior angle of a triangle...

Front 22

greater than either remote interior angle.

Back 22

Exterior Angle Theorem: An exterior angle of a triangle is...

Front 23

the angles opposite them are unequal in the same order.

Back 23

Thm. If two sides of a triangle are unequal...

Front 24

The sum of any two sides of a triangle is greater than the third side.

Back 24

Triangle Inequality Theorem