Mon 11/4

Boot-Up 11.4.13 / 6 min.

2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class:

a) ___ : ___: ___

b) ___ : ___: ___

Boot-Up 11.6.13 / 6 min.

2) Solve for each variable:1) Name any 3 of the 5 Congruence Theorems:

1) ______

2) ______

3) ______

4) ______

5) ______

Boot-Up 11.4.13 / 6 min.

2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class:

a) ___ : ___: ___

b) ___ : ___: ___

Boot-Up 11.4.13 / 6 min.

2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class:

a) ___ : ___: ___

b) ___ : ___: ___

Today’s Objective:

*SWBAT = Student Will Be Able To

6.1.1: SWBAT identify s by first determining that the s are ~ & that the ratio of corresponding sides is 1.

6.1.2: TSW develop shortcuts.

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.

OK, but what’s in it for me?

Find Lesson 6.1.1

6.1.1 6.1.2

6-1 6-11 6-2 a, b, d 6-12

6-13

6-1

What are the 3 similarity conditions we proved / studied?

1) AA 2) SAS 3) SSS

3 4

6 8

3-86Is SSA a valid similarity condition?

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

ABC ABD

The 2 s are NOT congruent 3-86

3-60

Facts

ConclusionSimilarity Condition

What does each row of ovals represent?

3-94

3 6 =

8 16 =

ABC KLM

B K 1 2

1 2

SAS

3-95

A K C L

ABC JKL

54

36

AAWhat’s wrong with this Flow Chart?

6-1

Are these s also ? Explain how you know.

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.)

6-2a

Are these s also ? Explain how you know.

BD BD

DBA

DBC

ABD

CBDAA

BDC

BDA

BD = BD = 1 1 =

6-2a

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

6-2b

BD = AC BC = BC B C

SAS

ABD

BCA

6-2c

4-68

6-2d

ABD

BAC

A B C D

AA

AB = AB ABD

BCA

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

6.1.2

6-11 6-12 6-13

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

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

2) SSS (Side-Side-Side)

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

3) ASA (Angle-Side-Angle)

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

AAS

4) AAS (Angle-Angle-Side)

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

HL (Right s Only)

5)

Why not AA for Congruence?

3-86Is SSA a valid similarity condition?

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

ABC ABD

The 2 s are NOT congruent 3-86

6-13Exit Ticket

4-68

8 min.

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

Do 5

5-2a

y3=tan 60

y3=1.732

=1 y 1.732 3

y 5.196=

y1=tan 60

y1=1.732

=1 y 1.732 1

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

32 + y2 = 62

9 + y2 = 36

y2 = 27

y2 = 27

y = 5.196

a2 + b2 = c2

12 + y2 = 22

1 + y2 = 4

y2 = 3

y2 = 3

y = 1.732

Did we get the same answers both ways?

5-2 b

36

= 12

Wed 11/6

Boot-Up 11.6.13 / 6 min.

2) Solve for each variable:1) Name any 3 of the 5 Congruence Theorems:

1) ______

2) ______

3) ______

4) ______

5) ______

Today’s Objective:

*TSW= The Student Will

6.1.4:

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

2) TSW practice identifying pairs of s and will contrast congruence arguments with similarity arguments.

Find Lesson 6.1.4

6.1.4

6-29 6-30 6-32

6-29

AB = FD

6-30

6-31

PQ = ST PRQ

TRS

PQR

TSR

P T

AAS

6-32a

AC = AC DCA

BAC

ABC

CDA

D B

AAS

6-32b

GHF

IHJ

FGH~

JIH

G I

AA~

6-32c

23

36

Neither ~ nor !

6-32d

SSS or HL !

Thu 10/31

29.2

4

2) Solve for each variable:1) Name any 3 of the 5 Congruence Theorems:

1) ______

2) ______

3) ______

4) ______

5) ______

Boot-Up 11.7.13 / 6 min.

Find Lesson 6.1.5

6.1.5 6.2.4 & 6.2.5

6-41 6-83 6-42 6-96 6-48 6-44

Today’s Objective:

*SWBAT = Student Will Be Able To

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.

6-41

If… alternate interior angles are equal,

then… lines are parallel.

6-41a

If… _______________________

then… ___________________

6-41a

If… parallel lines are intersected by a transversal,

then… the alternate interior s are =.

6-41b

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

2-46

Same Side Interiors Supplementary

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

What is the sum of s x & y?

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.

6-41c

Write the converse of the conditional statement below: If lines are parallel, then corresponding angles are equal.

Triangles congruent → corresponding sides are congruent.

6-42a

True False

Converse Statement: _______________________________

True False

Triangles congruent → corresponding angles are congruent.

6-42c

True False

Converse Statement: _______________________________

True False

Why not AA for Congruence?

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

6-42d

True False

Converse Statement: _______________________________

True False

6-48

6-44

AB = ED AC = DF BC = EF

ABC DEF

SSS

SAS60 60

5 cm

6-83ab

6-83cd

6-96ab

6-96c

Fri 11/1

Solve for all variables shown:Boot-Up 11.8.13 / 6 min.

Find Lesson 6.2.1

6.2.2 6.2.3

6-61a 6-73 6-61b 6-74 6-63 6-64

Today’s Objective:

*SWBAT = Student Will Be Able To

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

A

B

C

26

24

10 20

1223.32

30

1232.31

Rectangle= 30 x 24 = 720

120u2120u2

180u2

y

x

I

IVIII

II