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

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Mon 11/4

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  1. Mon 11/4

  2. 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.

  3. 1) Name any 3 of the 5 Congruence Theorems: 2) Solve for each variable: • ______ • ______ • ______ • ______ • ______ Boot-Up 11.6.13 / 6 min.

  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.

  5. 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. 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

  7. 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.

  8. Find Lesson 6.1.1

  9. 6-1

  10. What are the 3 similarity conditions we proved / studied? 2) SAS 3) SSS 1) AA 3 4 6 8

  11. Is SSAa valid similarity condition? 3-86

  12. 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

  13. What does each row of ovals represent? Facts Conclusion Similarity Condition 3-60

  14. 3 6 1 2 8 16 1 2 = = B  K ABC KLM SAS 3-94

  15. A  K C  L 54 ABC JKL What’s wrong with this Flow Chart? AA 36 3-95

  16. Are these salso ? Explain how you know. 6-1

  17. 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.)

  18. BDC   BDA DBA   DBC Are these salso ? Explain how you know. ABD  CBD 1 1 BD BD BD = BD = = AA 6-2a

  19. If you prove similarity by virtue of  congruence, how many sides do you have to prove are congruent to prove s are ? 6-2a

  20. BD = AC BC = BC BC ABD  BCA SAS 6-2b

  21. 6-2c

  22. 4-68 C D AB AB = AB ABD  BAC ABD  BCA AA 6-2d

  23. 6-3

  24. 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

  25. Find Lesson 6.1.2

  26. 6-11

  27. If 2 sides & the included of one are to the corresponding parts of another , the s are . 1) SAS (Side-Angle-Side) 6-12

  28. 2) SSS (Side-Side-Side) If 3 sides of 1 are to 3 sides of another , the s are .

  29. 3) ASA (Angle-Side-Angle) If 2 sand the included side of 1 are to the corresponding parts of another , the s are .

  30. 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

  31. 5) If the hypotenuse & leg of one right are to the corresponding parts of another right , the right s are . HL (Right s Only)

  32. Why not AA for Congruence?

  33. Is SSAa valid similarity condition? 3-86

  34. 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

  35. 6-13 Exit Ticket

  36. 4-68 8 min.

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

  38. 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…

  39. 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

  40. 5-2 b 3 6 1 2 =

  41. Wed 11/6

  42. 1) Name any 3 of the 5 Congruence Theorems: 2) Solve for each variable: • ______ • ______ • ______ • ______ • ______ Boot-Up 11.6.13 / 6 min.

  43. 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

  44. Find Lesson 6.1.4

  45. 6-29

  46. AB = FD 6-30

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