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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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Mon 11 4

Mon 11/4


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.


Mon 11 4

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

2) Solve for each variable:

  • ______

  • ______

  • ______

  • ______

  • ______

Boot-Up

11.6.13 / 6 min.


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.


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.


Mon 11 4

6.1.1: 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


Mon 11 4

OK, but what’s in it for 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.


Mon 11 4

Find Lesson 6.1.1


Mon 11 4

6-1


Mon 11 4

What are the 3 similarity conditions we proved / studied?

2) SAS

3) SSS

1) AA

3

4

6

8


Mon 11 4

Is SSAa valid similarity condition?

3-86


Mon 11 4

As you can see, even though side 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


Mon 11 4

What does each row of ovals represent?

Facts

Conclusion

Similarity

Condition

3-60


Mon 11 4

3

6

1

2

8

16

1

2

=

=

B  K

ABC KLM

SAS

3-94


Mon 11 4

A  K

C  L

54

ABC JKL

What’s wrong with this Flow Chart?

AA

36

3-95


Mon 11 4

Are these salso ?

Explain how you know.

6-1


Mon 11 4

There are 2 things you have to do to prove congruence. They are:

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.)


Mon 11 4

BDC

 BDA

DBA

 DBC

Are these salso ?

Explain how you know.

ABD

CBD

1

1

BD

BD

BD = BD

=

=

AA

6-2a


Mon 11 4

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

6-2a


Mon 11 4

BD = AC

BC = BC

BC

ABD

BCA

SAS

6-2b


Mon 11 4

6-2c


Mon 11 4

4-68

C D

AB

AB = AB

ABD

BAC

ABD

BCA

AA

6-2d


Mon 11 4

6-3


Mon 11 4

  • Two figures are congruent if they meet both the following conditions:

  • The two figures are similar, and

  • Their side lengths have a common ratio of 1


Mon 11 4

Find Lesson 6.1.2


Mon 11 4

6-11


Mon 11 4

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

1)

SAS

(Side-Angle-Side)

6-12


Mon 11 4

2)

SSS

(Side-Side-Side)

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


Mon 11 4

3)

ASA

(Angle-Side-Angle)

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


Mon 11 4

4)

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


Mon 11 4

5)

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

HL

(Right s Only)


Mon 11 4

Why not AA for Congruence?


Mon 11 4

Is SSAa valid similarity condition?

3-86


Mon 11 4

As you can see, even though side 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


Mon 11 4

6-13

Exit Ticket


Mon 11 4

4-68

8 min.


Mon 11 4

Do  5

Portfolio:

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


Mon 11 4

5-2a

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…


Mon 11 4

5-2a

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


Mon 11 4

5-2 b

3

6

1

2

=


Mon 11 4

Wed 11/6


Mon 11 4

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

2) Solve for each variable:

  • ______

  • ______

  • ______

  • ______

  • ______

Boot-Up

11.6.13 / 6 min.


Mon 11 4

6.1.4:

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


Mon 11 4

Find Lesson 6.1.4


Mon 11 4

6-29


Mon 11 4

AB = FD

6-30


Mon 11 4

PRQ

TRS

PQ = ST

P T

PQR

TSR

AAS

6-31


Mon 11 4

DCA

BAC

AC = AC

D B

 ABC

 CDA

AAS

6-32a


Mon 11 4

GHF

IHJ

GI

 FGH

~

 JIH

AA~

6-32b


Mon 11 4

2

3

3

6

Neither ~ nor !

6-32c


Mon 11 4

SSSorHL !

6-32d


Mon 11 4

Thu 10/31


Mon 11 4

2) Solve for each variable:

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

  • ______

  • ______

  • ______

  • ______

  • ______

29.24

Boot-Up

11.7.13 / 6 min.


Mon 11 4

Find Lesson 6.1.5


Mon 11 4

6.1.5: 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


Mon 11 4

If… alternate interior angles are equal,

then… lines are parallel.

6-41


Mon 11 4

If… _______________________

then… ___________________

6-41a


Mon 11 4

If… parallel lines are intersected by a transversal,

then… the alternate interior s are =.

6-41a


Mon 11 4

How are Jorge’s and Margaret’s statements related?  How are they different?

6-41b


Mon 11 4

What is the sum of s x & y?

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

Same Side Interiors

Supplementary

2-46


Mon 11 4

2-47


Mon 11 4

Conditional statements that have this relationship are called converses. 

Read M&M p.363.

6-41c


Mon 11 4

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


Mon 11 4

Triangles congruent   →   corresponding sides are congruent.

 True  False

Converse Statement: _______________________________

 True  False

6-42a


Mon 11 4

Triangles congruent   →   corresponding angles are congruent.

 True  False

Converse Statement: _______________________________

 True  False

6-42c


Mon 11 4

Why not AA for Congruence?


Mon 11 4

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

 True  False

Converse Statement: _______________________________

 True  False

6-42d


Mon 11 4

6-48


Mon 11 4

SAS

60

60

5 cm

BC = EF

AC = DF

AB = ED

 ABC   DEF

SSS

6-44


Mon 11 4

6-83ab


Mon 11 4

6-83cd


Mon 11 4

6-96ab


Mon 11 4

6-96c


Mon 11 4

Fri 11/1


Mon 11 4

Boot-Up

11.8.13 / 6 min.

Solve for all variables shown:


Mon 11 4

Find Lesson 6.2.1


Mon 11 4

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

Today’s

Objective:

*SWBAT= Student Will Be Able To


Mon 11 4

C

20

10

Rectangle

= 30 x 24

= 720

120u2

120u2

12

23.32

26

24

B

12

32.31

180u2

30

A


Mon 11 4

y

II

I

x

III

IV


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