6.1 Inequalities and Indirect Proofs

Up until now we have dealt with sides and angles that are ___________ and have used the properties of _________ in our proofs.

Now we will deal with _________ sides and angles. We will be using properties of ______________.

Property of Inequality

(All of these)

Exterior Angle Theorem: ____________

__________________________________

__________________________________

__________________________________

1

2

3

: ;

Prove :

Given AC BC CE CD

AE BD

A

B

C

D

E

: 1 is and exterior angle

Prove : 1 ; 1

Given

D E

F

D

E

1

: 2> 1

Prove : 2 4

Given

1

3

2

4

6.3 Indirect Proof

We will be using __________________

_____________________________. Lets look at an example.

Lets suppose after walking home, Joe enters the house carrying a dry umbrella. You can conclude that it is not raining outside. Why?

________________________________

________________________________

Steps for solving an Indirect Proof:

•___________________________________________________________________

•___________________________________________________________________

•_______________________________________________________________________________________________________________________________________

Lets try one, these will be written as a paragragh.

: is a trapezoid

Prove: PQ SR

Given SRQP

S R

P Q

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

6.4

Inequalities

Inequalities for one Triangle

Theorem 6.2: __________________________

________________________________________

________________________________________

________________________________________

Theorem 6.3: __________________________

________________________________________

________________________________________

________________________________________

A

B

C

10 12

18

List angles from Largest to smallest:

____ ____ ____

61

60 59

A

BC

List sides from Largest to smallest:

____ ____ ____

Corollary 1: ______________________________

________________________________________

________________________________________

Theorem 6.4: ___________________________

________________________________________

________________________________________

When given 2 sides of a triangle you can find a range that the third side will be between.

•_____________________________________

______________________________________

______________________________________

10,12, ________

25,26, ________

, 2, _______y y

Find out if each is a triangle, given the sides:

1. 6,8,20

2. 2.5, 5, 4.1

3. 3, 4, 5

4. 6, 4, 2

5. 6, 5, 6

80

x x-10

B

AC

Which side is the longest?

A

B

C

D61

59

60

61

60

59

____ ____ ____ ____ ____

6.5 Inequalities for 2 Triangles

Theorem 6-5: SAS Inequality

______________________________________________________________________________________________________________________________________________________________________________________________________________________________

55 34

A B

Theorem 6-5: SSS Inequality

______________________________________________________________________________________________________________________________________________________________________________________________________________________________

55 34

A B

Example:

What can you deduce?

: ; 1 2Given RS RT

1

2R

T

V

S

•____________

•___________________________________________________

Example:

What can you deduce?

: Marked on DrawingGiven

R

T

V

S

•______________

•______________

Y

X

12

14

Example:

What can you deduce?

: Marked on DrawingGiven

5

10

•______________

•______________10

1

6

2