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Mon 11/4

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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:

- ______
- ______
- ______
- ______
- ______

Boot-Up

11.6.13 / 6 min.

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 2 of the 4 Pythagorean Triples discussed in class:

2) Solve for each variable:

a) ___ : ___: ___

b) ___ : ___: ___

Boot-Up

11.4.13 / 6 min.

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

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.

Find Lesson 6.1.1

6-1

What are the 3 similarity conditions we proved / studied?

2) SAS

3) SSS

1) AA

3

4

6

8

Is SSAa valid similarity condition?

3-86

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

What does each row of ovals represent?

Facts

Conclusion

Similarity

Condition

3-60

3

6

1

2

8

16

1

2

=

=

B K

ABC KLM

SAS

3-94

A K

C L

54

ABC JKL

What’s wrong with this Flow Chart?

AA

36

3-95

Are these salso ?

Explain how you know.

6-1

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.)

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 congruence, how many sides do you have to prove are congruent to prove s are ?

6-2a

BD = AC

BC = BC

BC

ABD

BCA

SAS

6-2b

6-2c

4-68

C D

AB

AB = AB

ABD

BAC

ABD

BCA

AA

6-2d

6-3

- 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

Find Lesson 6.1.2

6-11

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

1)

SAS

(Side-Angle-Side)

6-12

2)

SSS

(Side-Side-Side)

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

3)

ASA

(Angle-Side-Angle)

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

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

5)

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

HL

(Right s Only)

Why not AA for Congruence?

Is SSAa valid similarity condition?

3-86

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

6-13

Exit Ticket

4-68

8 min.

Do 5

Portfolio:

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

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…

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

5-2 b

3

6

1

2

=

Wed 11/6

1) Name any 3 of the 5 Congruence Theorems:

2) Solve for each variable:

- ______
- ______
- ______
- ______
- ______

Boot-Up

11.6.13 / 6 min.

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

Find Lesson 6.1.4

6-29

AB = FD

6-30

PRQ

TRS

PQ = ST

P T

PQR

TSR

AAS

6-31

DCA

BAC

AC = AC

D B

ABC

CDA

AAS

6-32a

GHF

IHJ

GI

FGH

~

JIH

AA~

6-32b

2

3

3

6

Neither ~ nor !

6-32c

SSSorHL !

6-32d

Thu 10/31

2) Solve for each variable:

1) Name any 3 of the 5 Congruence Theorems:

- ______
- ______
- ______
- ______
- ______

29.24

Boot-Up

11.7.13 / 6 min.

Find Lesson 6.1.5

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

If… alternate interior angles are equal,

then… lines are parallel.

6-41

If… _______________________

then… ___________________

6-41a

If… parallel lines are intersected by a transversal,

then… the alternate interior s are =.

6-41a

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

6-41b

What is the sum of s x & y?

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

Same Side Interiors

Supplementary

2-46

2-47

Conditional statements that have this relationship are called converses.

Read M&M p.363.

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 → corresponding sides are congruent.

True False

Converse Statement: _______________________________

True False

6-42a

Triangles congruent → corresponding angles are congruent.

True False

Converse Statement: _______________________________

True False

6-42c

Why not AA for Congruence?

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

True False

Converse Statement: _______________________________

True False

6-42d

6-48

SAS

60

60

5 cm

BC = EF

AC = DF

AB = ED

ABC DEF

SSS

6-44

6-83ab

6-83cd

6-96ab

6-96c

Fri 11/1

Boot-Up

11.8.13 / 6 min.

Solve for all variables shown:

Find Lesson 6.2.1

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

C

20

10

Rectangle

= 30 x 24

= 720

120u2

120u2

12

23.32

26

24

B

12

32.31

180u2

30

A

y

II

I

x

III

IV