is x greater at 1:00 or 3:00? lesson 5-5 inequalities involving two triangles what part of the clock...

Is x greater at 1:00 or 3:00?

Lesson 5-5 Inequalities involving two trianglesInequalities involving two trianglesInequalities involving two trianglesInequalities involving two triangles

What part of the clock affects the length of x?

It’s greater at 3:00

The angle between the hour hand and minute hand

Hinge Theorem

When you close a door, the anglebetween the door and the frame

(at the hinge )gets smaller.

If two sides of one triangle are congruent to two sides of another triangle,

and the included angle of the first is larger than the included angle of the second,

then the third side of the first is longer than the third side of the second.

V

X

W

88

R

S

T

35XW XW>

Lesson 5-5

Converse Of Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle,

and the third side of the first is longer than the third side of the second,

then the included angle of the first is larger than the included angle of the

second.

D

EF

9

A

C B

12C F>

Lesson 5-5

Using Hinge Theorem and its ConverseLesson 5-5

Using Hinge Theorem and its Converse

What inequality relates SK and YU?

SK YU>

Lesson 5-5

Using Hinge Theorem and its Converse

What inequality relates LN and OQ?

LN OQ>

Lesson 5-5

Using Hinge Theorem and its Converse

Complete the statement with < or > Explain

CBD ____ ADB mm >

Lesson 5-5

A

D

B

C

34

33

Using Hinge Theorem and its ConverseLesson 5-5

AB FD>

10)

Using Hinge Theorem and its ConverseLesson 5-5

BDC FDB<

11)

Using Hinge Theorem and its ConverseLesson 5-5

FBA DBF>

12)

Using Hinge Theorem and its ConverseLesson 5-5

AD DC>

13)

Using Hinge Theorem and its ConverseLesson 5-5

<

14)

OC OA

Using Hinge Theorem and its ConverseLesson 5-5

>

15)

AOD AOB

Using Hinge Theorem and its ConverseLesson 5-5

1023 x

123 x

+2 +2

3 3

4x

16)

Using Hinge Theorem and its ConverseLesson 5-5

1008205 xx

100203 x

-8x-8x

1203 x

18)

- 20

40x

-3 -3

A

B

M

C

12

2051 xmGiven 10082 xm

BCAC

- 20

1203 x 01008 x

1008 x

5.12x

+ 100

8 8

+ 100

BONUSLesson 5-5

20)

D

B

CA

2

1

CDAB Given

ADBC Prove

Statements Reasons

CDAB

ADBC given

21 mm Exterior angle theorem

ADBC Hinge theorem

Homework

Page 271

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Lesson 5-5