Mon 11/4

Boot-Up / 6 min. 2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class: a) ___ : ___: ___ b) ___ : ___: ___

Boot-Up / 6 min. 2) Solve for each variable: 1) Name any 3 of the 5  Congruence Theorems: 1)______ 2)______ 3)______ 4)______ 5)______

Boot-Up / 6 min. 2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class: a) ___ : ___: ___ b) ___ : ___: ___

Boot-Up / 6 min. 2) Solve for each variable:1) Name any 2 of the 4 Pythagorean Triples discussed in class: a) ___ : ___: ___ b) ___ : ___: ___

Today’sObjective: * SWBAT = S tudent W ill B e A ble T o 6.1.1: SWBAT identify   s by first determining that the  s are ~ & that the ratio of corresponding sides is : 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  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  34 68

3-86 Is 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 Conclusion Similarity Condition What does each row of ovals represent?

= 8 16 =  ABC   KLM  B   K SAS 

3-95  A   K  C   L  ABC   JKL 54  36  AA  What’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  DBA   DBC  ABD   CBD AA   BDC   BDA BD = BD = 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

d  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  6-11  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?

3-86 Is 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

6-13 Exit Ticket

min.

Portfolio: Do a or b or (c & d & e) + f. Do  5

5-2a y3y3 = tan 60  y3y3 = =1 y y = y1y1 = tan 60  y1y1 = =1 y y = Hey, Bub: Divide these rises (5.196  1.732), what do you get? Now divide the runs…

5-2a a 2 + b 2 = c y 2 = y 2 = 36 y 2 = 27  y 2 =  27 y = a 2 + b 2 = c y 2 = y 2 = 4 y 2 = 3  y 2 =  3 y = Did we get the same answers both ways?

5-2 b 3636 = 1212

Wed 11/6

Boot-Up / 6 min. 2) Solve for each variable: 1) Name any 3 of the 5  Congruence Theorems: 1)______ 2)______ 3)______ 4)______ 5)______

Today’sObjective: * TSW = T he S tudent W ill 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  6-29  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 2323  3636 Neither ~ nor  !

6-32d SSS or HL !

Thu 10/31

29.24  2) Solve for each variable: 1) Name any 3 of the 5  Congruence Theorems: 1)______ 2)______ 3)______ 4)______ 5)______ Boot-Up / 6 min.

Find Lesson &  6-41  6-83  6-42  6-96  6-48  6-44

Today’sObjective: * SWBAT = S tudent W ill B e A ble T o 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 Interior  s 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 c

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 = EDAC = DF BC = EF  ABC   DEF SSS  SAS  60  5 cm

6-83ab

6-83cd

6-96ab

6-96c

Fri 11/1

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

Find Lesson  6-61a  6-73  6-61b  6-74  6-63  6-64

Today’sObjective: * SWBAT = S tudent W ill B e A ble T o 6.2.2: SWBAT review area & perimeter of a , Trigonometry, Pythagorean Theorem, & the Triangle Angle Sum Theorem.

A B C Rectangle = 30 x 24 = u 2 180u 2

y x I IVIII II