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Transcript
Mrs. Jones’s Mathography I was born as Jenny Dai, but since my marriage to Mr. Matt Jones 196 years ago, I became Mrs. Jones. That is also what I like to be called. I live with 3 64 others at my home: my husband Matt, my daughters Eden and Klara, and my mother Shunu. Matt has a Ph. D in Mathematics and is a professor at Cal State Dominguez Hills (home of the LA Galaxy soccer team). Eden was born on the (n1) th day where 180(n1 2) 4500 in the [n2] th month where e n2 2981of the year (2*103)+3. Klara was born on the (n3) th day where 180(n 3 2) 2520in the (n4)th month where log 5 n 4 1 of the year (2*103)+8. Taiwanese, and English at home, and am currently trying to teach all I speak Mandarin, languages to Eden and Klara. My interests, talents, [π] and hobbies include country line dancing, reading, traveling, collecting college t-shirts (I have ( [15.6 ] ) in my collection), and eating (In the last [19.1 ] months, I have eaten at [115.9 ] different restaurants, [34.1 ]of them multiple times). I am proud of being a math teacher at Kennedy, where I graduated in 25(80-π)+25π –7 (before all of you were born). My birthday is the [9.3 ] th day of the [1.3 ] th month, in the year of 25(80-π)+25π -25. I was a good math student from kindergarten through UCLA (where I received my bachelors and masters degrees). I liked when teachers tried to make math make sense and not just make me blindly follow procedures. I also enjoyed seeing some of the reallife applications of math. As a teacher, I will strive to make sure both happen in my classroom. This year I am teaching geometry and finite/trig. This is my (23 +22+21+20)th year of teaching, but only my (32)th year at Kennedy. I have taught every math class from algebra through calculus, starting in the year (2*103)-3. I worked at Santa Monica High School and Birmingham High School before coming to Kennedy. I have had many of you or your older siblings/cousins in previous classes and am looking forward to knowing each of you better throughout the year! Key: [ ] means greatest integer function You are only eligible for extra credit if you are present on Friday 11/22 and Monday 12/2 and get at least 3 out of 4 on the homework assignment from Friday 11/22. To earn 4 points extra credit: print out and translate Mrs. Jones’s mathography. To earn an additional 10 points extra credit: write your own mathography in math code and provide answers on a different page. Turn in everything on Monday 12/2. 1 McDougal Honors Geometry chapter 6 notes 6.1 Ratios, proportions, and the geometric mean Day 1: Read section 6.1 and take notes on pg 356-359. Do guided practice 1-11 all. Day 2: Pg 360 #7-71 odds. 2 6.2 Use proportions to solve geometry problems, pg. 367 #3-37 odds TK#50: Properties of proportions The geometric mean of 2 positive numbers a and b is the positive number x such that a x . So x2=ab and x ab. x b 1. Cross product property. In a proportion, the product of the extremes equals the product of the means. If 2. Reciprocal property. If 2 ratios are equal, then their reciprocals are also equal. If 3. a c where b≠0 and d≠0, then ad=bc. b d a c b d , then . b d a c If we swap the means of a proportion, then we form another true proportion. If a c a b , then . b d c d 4. In a proportion, if we add the value of each ratio’s denominator to its numerator, then we form another true proportion. If ab cd . b d a c , then b d Guided practice 1-4. Example 5. (If time) Prove: If a c ab cd , then . b d b d 3 6.3 Use similar polygons, pg 376 #5-33 odds, 36, 39 (on graph paper) 2 polygons are similar (~) if corresponding angles are congruent and corresponding sides are proportional. If ABCD~EFGH, then corresponding angles are congruent: A E , B F , C G, D H and corresponding sides are AB BC CD DA . In writing the similarity statements, order is proportional: EF FG GH HE crucial! B F A D E G H C TK#51: Similar polygons Any corresponding 1-dimensional part (length, perimeter, etc) of similar polygons is equal to the scale factor. Guided practice 1,4-6. __________ Quiz Review pg. 380 #1-7 __________Quiz 6.1-6.3. Hwk: Activity on the top of pg 381: Angles and similar triangles (need protractor and ruler). Steps 1-4. Draw conclusions 1,2. 4 6.4 Prove triangles similar by AA, pg 384#3-29 odds, 30-36E Turn in Activity 6.4. TK#52: AA similarity postulate: If 2 angles in one triangle are congruent to 2 angles in another triangle, then the 2 triangles are similar. Since J X , K Y , then ∆JKL~∆XYZ by AA∆~Post. K Y L Z X J Guided practice 2, 4. 5 6.5 Prove triangles similar by SSS and SAS TK#53: SSS Similarity Thm: If all 3 corresponding sides of two triangles are proportional, then the triangles are similar. If AB BC CD , then ∆ABC~∆RST RS ST TR by SSS∆~ Thm. A R C T S B TK#54: SAS Similarity Thm: If 2 sides of one triangle are proportional to the corresponding 2 sides of another triangle and the included angles are congruent, then the two triangles are similar. If JK KL and K Y , then ∆JKL~∆XYZ by XY YZ SAS∆~ Thm. K Y L Z X J Find x to make ∆JKL~∆MYZ Example K 3(x-2) Y 12 L 21 Z x+6 20 30 M J Guided practice 1-3. 6 If time: prove guided practice 4. Prove the SSS∆~ Thm. 6.5 one day: pg 391 #3-37 odds or 6.5 day 1 pg 391 #3-27 odds, 35, 39-44 (bring compass and straightedge tomorrow) 6.5 day 2 pg 393 #18-34E, 37, 38 (bring compass and straightedge tomorrow) 7 6.6 Use proportionality thms TK#55: Triangle Proportionality Thm: If a line parallel to one side of a triangle intersects the other 2 sides, then it divides the 2 sides proportionally. If TU || QS , then RT RU . TQ US Q T R S U TK#56: Converse of Triangle Proportionality Thm: If a line divides 2 sides of a triangle proportionally, then it is parallel to the third side. If RT RU , then TU || QS . TQ US TK#57: Extended Proportionality Thm: If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally. r s t Y U V UW VX WY XZ l W X Z m TK#58: Angle Bisector Proportionality Thm: If a ray bisects an angle of a triangle, then it divides the opposite side into the same proportion as the 2 sides that form the angle. AD AC DB BC A D C B Example 4. Guided practice 2, 3. 6.6 day 1 pg 400#3-19 odds, 22, 27 (need compass and straightedge) 6.6 day 2 pg 400#12-20E, 21, 23-25 (need compass and straightedge) 8 Dilation Activity 6.7 on pg 408 Steps 1-4. Draw conclusions 1,2. (Need graph paper, compass, and ruler.) Hwk: Ch 6 review pg 418 #2-18 all. Print out Ch 7 notes. 6.7 Perform similarity transformations (Need graph paper). Pg 412 #3-21 odds (skip 17) Turn in Activity 6.7 and ch 6 review. With dilation: If 0<k<1, reduction. If k>1, enlargement. Guided practice 2, 3. _______ Ch 6 Test, Collect TK#1-58. 9