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# Mon 11/4 - PowerPoint PPT Presentation

Mon 11/4. 1) Name any 2 of the 4 Pythagorean Triples discussed in class:. 2) Solve for each variable:. a) ___ : ___: ___ b) ___ : ___: ___. Boot-Up 11.4.13 / 6 min. 1) Name any 3 of the 5  Congruence Theorems:. 2) Solve for each variable:. ______ ______ ______ ______

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2) Solve for each variable:

a) ___ : ___: ___

b) ___ : ___: ___

Boot-Up

11.4.13 / 6 min.

1) Name any 3 of the 5 class:Congruence Theorems:

2) Solve for each variable:

• ______

• ______

• ______

• ______

• ______

Boot-Up

11.6.13 / 6 min.

2) Solve for each variable:

a) ___ : ___: ___

b) ___ : ___: ___

Boot-Up

11.4.13 / 6 min.

2) Solve for each variable:

a) ___ : ___: ___

b) ___ : ___: ___

Boot-Up

11.4.13 / 6 min.

6.1.1: class:SWBAT identify sby first determining that the s are ~ & that the ratio of corresponding sides is 1.

6.1.2: TSW develop  shortcuts.

Today’s

Objective:

*SWBAT= Student Will Be Able To

OK, but what’s in it for class:me?

Fields that use trigonometry or trigonometric functions include:

Astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography & game development.

6-1 class:

2) SAS

3) SSS

1) AA

3

4

6

8

Is class:SSAa valid similarity condition?

3-86

As you can see, even though side class:BC = BD , this side length is able to swivel such that 2 non-congruent sare created even though they have 2  sides and a , non-included . (SSA)

ABC ABD

The 2 s are NOT congruent

3-86

Facts

Conclusion

Similarity

Condition

3-60

3 class:

6

1

2

8

16

1

2

=

=

B  K

ABC KLM

SAS

3-94

class:A  K

C  L

54

ABC JKL

What’s wrong with this Flow Chart?

AA

36

3-95

Are these class:salso ?

Explain how you know.

6-1

1) Prove Similarity. (That they’re the Same Shape.)

2) Prove Side Lengths have a common ratio of 1. (That they’re the Same Size.)

are:BDC

 BDA

DBA

 DBC

Are these salso ?

Explain how you know.

ABD

CBD

1

1

BD

BD

BD = BD

=

=

AA

6-2a

If you prove similarity by virtue of are: congruence, how many sides do you have to prove are congruent to prove s are ?

6-2a

BD = AC are:

BC = BC

BC

ABD

BCA

SAS

6-2b

6-2c are:

4-68 are:

C D

AB

AB = AB

ABD

BAC

ABD

BCA

AA

6-2d

6-3 are:

Find Lesson 6.1.2 conditions:

6-11 conditions:

If conditions:2 sides & the included of one are to the corresponding parts of another , the s are .

1)

SAS

(Side-Angle-Side)

6-12

2 conditions:)

SSS

(Side-Side-Side)

If 3 sides of 1 are to 3 sides of another , the s are .

3) conditions:

ASA

(Angle-Side-Angle)

If 2 sand the included side of 1 are to the corresponding parts of another , the s are .

4) conditions:

If 2 s and the non-included side of one are to the corresponding parts of another , the s are .

AAS

(Angle-Angle-Side)

AAS

5) conditions:

If the hypotenuse & leg of one right are to the corresponding parts of another right , the right s are .

HL

(Right s Only)

Is conditions:SSAa valid similarity condition?

3-86

As you can see, even though side conditions:BC = BD , this side length is able to swivel such that 2 non-congruent sare created even though they have 2  sides and a , non-included . (SSA)

ABC ABD

The 2 s are NOT congruent

3-86

6-13 conditions:

Exit Ticket

4-68 conditions:

8 min.

Do conditions: 5

Portfolio:

Do a or b or (c & d & e) + f.

5-2a conditions:

y

3

y

1

tan 60

=

tan 60

=

y

3

y

1

1.732

=

1.732

=

1  y

=

1.732  3

1  y

=

1.732  1

y

=

5.196

y

1.732

=

Hey, Bub: Divide these rises (5.196  1.732), what do you get? Now divide the runs…

5-2a conditions:

a2+ b2 = c2

a2+ b2 = c2

12+ y2 = 22

32+ y2 = 62

1+ y2 = 4

9+ y2 = 36

y2 = 3

y2 = 27

Did we get the same answers both ways?

y2 = 3

y2 = 27

y = 1.732

y = 5.196

5-2 b conditions:

3

6

1

2

=

Wed 11/6 conditions:

1) Name any 3 of the 5 conditions:Congruence Theorems:

2) Solve for each variable:

• ______

• ______

• ______

• ______

• ______

Boot-Up

11.6.13 / 6 min.

6.1.4: conditions:

1) TSW extend their use of flowcharts to document  facts.

2) TSW practice identifying pairs of  sand will contrast congruence arguments with similarity arguments.

Today’s

Objective:

*TSW= The Student Will

Find Lesson 6.1.4 conditions:

6-29 conditions:

AB = FD conditions:

6-30

conditions:PRQ

TRS

PQ = ST

P T

PQR

TSR

AAS

6-31

conditions:DCA

BAC

AC = AC

D B

 ABC

 CDA

AAS

6-32a

conditions:GHF

IHJ

GI

 FGH

~

 JIH

AA~

6-32b

2 conditions:

3

3

6

Neither ~ nor !

6-32c

SSS conditions:orHL !

6-32d

Thu 10/31 conditions:

2) Solve for each variable: conditions:

1) Name any 3 of the 5 Congruence Theorems:

• ______

• ______

• ______

• ______

• ______

29.24

Boot-Up

11.7.13 / 6 min.

Find Lesson 6.1.5 conditions:

6.1.5: conditions:SWBAT recognize the converse relationship between conditional statements, & will then investigate the relationship between the truth of a statement & the truth of its converse.

Today’s

Objective:

*SWBAT= Student Will Be Able To

If… conditions:alternate interior angles are equal,

then… lines are parallel.

6-41

If… conditions:_______________________

then… ___________________

6-41a

If… conditions:parallel lines are intersected by a transversal,

then… the alternate interior s are =.

6-41a

What is the sum of are they different?s x & y?

Rianna says something’s wrong with this picture. Do you agree?

Same Side Interiors

Supplementary

2-46

2-47 are they different?

Conditional statements that have this relationship are called converses.

6-41c

Conditional statements that have this relationship are called converses.

• Write the converse of the conditional statement below:

• If lines are parallel, then corresponding angles are equal.

6-41c

Triangles congruent  called  →   corresponding sides are congruent.

 True  False

Converse Statement: _______________________________

 True  False

6-42a

Triangles congruent  called  →   corresponding angles are congruent.

 True  False

Converse Statement: _______________________________

 True  False

6-42c

A shape is a rectangle   called →   the area of the shape is b h.

 True  False

Converse Statement: _______________________________

 True  False

6-42d

6-48 called

SAS called 

60

60

5 cm

BC = EF

AC = DF

AB = ED

 ABC   DEF

SSS

6-44

6-83ab called

6-83cd called

6-96ab called

6-96c called

Fri 11/1 called

Boot-Up called

11.8.13 / 6 min.

Solve for all variables shown:

6.2.2: called SWBAT review area & perimeter of a , Trigonometry, Pythagorean Theorem, & the Triangle Angle Sum Theorem.

Today’s

Objective:

*SWBAT= Student Will Be Able To

C called

20

10

Rectangle

= 30 x 24

= 720

120u2

120u2

12

23.32

26

24

B

12

32.31

180u2

30

A

y called

II

I

x

III

IV