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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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slide2

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.

slide3

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

2) Solve for each variable:

  • ______
  • ______
  • ______
  • ______
  • ______

Boot-Up

11.6.13 / 6 min.

slide4

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.

slide5

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.

slide6

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

slide7

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.

slide12

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

slide13

What does each row of ovals represent?

Facts

Conclusion

Similarity

Condition

3-60

slide14

3

6

1

2

8

16

1

2

=

=

B  K

ABC KLM

SAS

3-94

slide15

A  K

C  L

54

ABC JKL

What’s wrong with this Flow Chart?

AA

36

3-95

slide16

Are these salso ?

Explain how you know.

6-1

slide17

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.)

slide18

BDC

 BDA

DBA

 DBC

Are these salso ?

Explain how you know.

ABD

CBD

1

1

BD

BD

BD = BD

=

=

AA

6-2a

slide19

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

6-2a

slide20

BD = AC

BC = BC

BC

ABD

BCA

SAS

6-2b

slide22

4-68

C D

AB

AB = AB

ABD

BAC

ABD

BCA

AA

6-2d

slide24

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
slide27

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

1)

SAS

(Side-Angle-Side)

6-12

slide28

2)

SSS

(Side-Side-Side)

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

slide29

3)

ASA

(Angle-Side-Angle)

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

slide30

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

slide31

5)

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

HL

(Right s Only)

slide34

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

slide35

6-13

Exit Ticket

slide40

4-68

8 min.

slide41

Do  5

Portfolio:

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

slide42

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…

slide43

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

slide44

5-2 b

3

6

1

2

=

slide46

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

2) Solve for each variable:

  • ______
  • ______
  • ______
  • ______
  • ______

Boot-Up

11.6.13 / 6 min.

slide47

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

slide51

PRQ

TRS

PQ = ST

P T

PQR

TSR

AAS

6-31

slide52

DCA

BAC

AC = AC

D B

 ABC

 CDA

AAS

6-32a

slide53

GHF

IHJ

GI

 FGH

~

 JIH

AA~

6-32b

slide54

2

3

3

6

Neither ~ nor !

6-32c

slide57

2) Solve for each variable:

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

  • ______
  • ______
  • ______
  • ______
  • ______

29.24

Boot-Up

11.7.13 / 6 min.

slide59

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

slide60

If… alternate interior angles are equal,

then… lines are parallel.

6-41

slide61

If… _______________________

then… ___________________

6-41a

slide62

If… parallel lines are intersected by a transversal,

then… the alternate interior s are =.

6-41a

slide64

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

slide66

Conditional statements that have this relationship are called converses. 

Read M&M p.363.

6-41c

slide67

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

slide68

Triangles congruent   →   corresponding sides are congruent.

 True  False

Converse Statement: _______________________________

 True  False

6-42a

slide69

Triangles congruent   →   corresponding angles are congruent.

 True  False

Converse Statement: _______________________________

 True  False

6-42c

slide71

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

 True  False

Converse Statement: _______________________________

 True  False

6-42d

slide74

SAS

60

60

5 cm

BC = EF

AC = DF

AB = ED

 ABC   DEF

SSS

6-44

slide80

Boot-Up

11.8.13 / 6 min.

Solve for all variables shown:

slide82

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

slide84

C

20

10

Rectangle

= 30 x 24

= 720

120u2

120u2

12

23.32

26

24

B

12

32.31

180u2

30

A

slide86

y

II

I

x

III

IV

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