Homework Review: 4-17 to 4-22

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1 Homework Review: 4-17 to Since the slope ratio for , AB 50'. The slope ratio for , so BC 4', segment AB is actually longer a. 12 b. Yes c. 6/12 = 1/2; 8/12 = 2/3

2 Warm-Up: In your spiral, copy the diagrams. Determine which similarity conjectures (AA, SSS, or SAS ) could be used to establish that the following pairs of triangles are similar. List as many as you can.

4 Quiz Time: 10/25 Do only your own work. Show all work. Use only your own INB, pencil, eraser, scientific calculator. No phones out when quizzes are out Turn quiz over when finished for me to collect & preview Lesson If you want to access accommodations for extended time/alternative location, please write Room Number & date/time where & when you will complete the quiz, such as, "Finish in Rm 704, 3:35."

6 4-10 Roll & Win! You begin the game Roll and Win by picking a number. Then you roll two regular dice, each numbered 1 through 6, and add the numbers that come up together. If the sum is the number you chose, you win a point. For example, if you choose 11, and a 6 and a 5 are rolled, you win! a. What is the sample space? b. Make a model of all the possible outcomes like the one at right. Copy and complete this table of sums on your paper. Are each of the outcomes in this table equally likely? c. What is P(even)? P(10)? P(15)? d. Which sum is the most likely result? What is the probability of rolling that sum?

7 Objective: Use slope ratios for new angles in order to solve for missing side lengths of triangles.

8 Objective: Use slope ratios for new angles in order to solve for missing side lengths of triangles.

9 CW: 4-23 to 4-26

10 Go to class website Select Technology etools Scroll down to, & select, Slope Ratios (Desmos) Choose the demo

11 CW: 4-23 to 4-25 Write a proportion!

12 CW: 4-23 to 4-25

13 CW: 4-23 to 4-25

14 CW: 4-23 to 4-25

15 CW: 4-23 to 4-26

17 4-25 If you have not done so already, add any and all slope ratios with their corresponding angles to your Trig Table Toolkit. Be sure to draw and label the triangle for each new angle. Summarize your findings which slope triangles did not work? Do you see any patterns? Note: we will learn a method soon for generating moreaccurate & -precise values for these slope ratios; until then, we will use these values from the e-tool &/or the RP.

19 INB 41 (Flap)

20 Objective: Use slope ratios for new angles in order to solve for missing side lengths of triangles.

21 HW: 4-27 to 4-32; Finish 4-24 if not done; LL 4-26 as flap on INB p41; Chapter 3 Quiz 10/27; Download a clinometer app, eg, ihandy Level

22 CPM 223 INB 42 Math Notes: Arithmetic Sequences An ordered list of numbers is a sequence Each number in the sequence is a term 1, 5, 9, 13, Variables with subscripts are used to label terms: a is the variable used to label the sequence a 1 = 1 a 3 = 9 In the sequence above, there is a common difference d = 4 this is an arithmetic sequence An explicit formula tells you exactly how to find any specific term in the sequence. a n = a 1 + (n 1)d n = term number d = common difference. A recursive formula tells first term and how to get from one term to the next. a n+1 = a n + d a 1 = some specific value d = common difference. For the sequence above:1, 5, 9, explicit: a n = 1 + (n 1)(4) recursive: a 1 = 1, a n+1 = a n + 4. a 2 = a = a 3 = a = 5 + 4

23 CPM 223 Math Notes: Geometric Sequences INB 43 In the sequence 2, 6, 18, 54,..., there is a common ratio between the successive terms. 2, 6, 18, 54,... This is called a geometric sequence The explicit formula tells you exactly how to find any specific term in the sequence. a n = a 1 r n 1 n = term number r = common ratio. The recursive formula gives first term and how to get from one term to the next term. a n+1 = a n r a 1 = some specific value r = common ratio. For the sequence 2, 6, 18, 54,... explicit a 2 = a 1 r n 1 recursive a n+1 = a n r a 2 = 2 3 n 1 a 1 = 2, r = 3 a 2 = a (1+1) = a 1 3 a 2 = 2 3 a 2 = 2 3 a 2 = 6 a 2 = 6 In each case, successively replacing n by 1, 2, 3,... gives the terms of the sequence.

8.1.2 What is its measure?

8.1.2 What is its measure? Interior Angles of a Polygon Objective: Students will learn how to find the sum of the interior angles of a polygon and will be able CCSS: G-GMD.1 Mathematical Practices: reason