Day Opener. a) The midsegment of a trapezoid is 10 inches long. One base is 19 inches long. How long is the other base? 128
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1 Day Opener a) The midsegment of a trapezoid is 10 inches long. One base is 19 inches long. How long is the other base? 128 b) Solve for every unknown part. 72 C c) AB = 5. CD = 7. Which chord is closer to the center? Why? d) How much does the average American wedding cost? A B D $22,360 1
2 2. Pass Back Tests 15 b 3 d 65 a c 20 2
3 2. Pass Back Tests 15 d 23 a c b 3
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19 2. Notes Construct a circle. 180 Conjecture 36: Inscribed Semicircles Conjecture Angles inscribed in a semicircle measure 90. x y z 19
20 2. Notes Construct a circle Conjecture 37: Cyclic Quadrilateral Conjecture The opposite angles of a cyclic quadrilateral are supplementary
21 3. Classwork pg. 322 // #
22 Day Opener a) An exterior angle of a regular polygon is one-ninth one of the interior angles. How many sides does it have? Talk about how circumference, diameter, and radius b) What is the are three average friends, number from biggest of guests to smallest. at an What s American wedding? the relationship between circumference & diameter (times pi), what s the relationship between circumference & radius (there is none) 9x x 125; Re-run the opener problem using 1/6. Impossible. 22
23 2. Pi. Tell me five things about pi. Pi: The ratio of the circumference of a circle to its diameter. circumference diameter circumference diameter = π 23
24 2. Pi. Tell me five things about pi. Pi: The ratio of the circumference of a circle to its diameter =
25 47 2. Pi. Tell me five things about pi. Pi: The ratio of the circumference of a circle to its diameter =
26 2. Pi. Four formulas. C D = π C = π (2R) C = π D A = π (R) 2 26
27 2. Pi. I bring home 90 feet of fencing for a circular pen to corral my 4-H pig, Penelope. 1. What kind of diameter does this give me? 2. Penelope needs at least 700 square feet to, y know, do all of her pig stuff in. Are we good? 27
28 2. Pi. Four formulas. C D = π C = π (2R) C = π D A = π (R) 2 28
29 2. Pi. I bring home 90 feet of fencing for a circular pen to corral my 4-H pig, Penelope. 1. What kind of diameter does this give me? 2. Penelope needs at least 700 square feet to, y know, do all of her pig stuff in. Are we good? C = π D 90 = π D 90 = (3.14) D 28.7 feet = D 29
30 2. Pi. Four formulas. C D = π C = π (2R) C = π D A = π (R) 2 30
31 2. Pi. I bring home 90 feet of fencing for a circular pen to corral my 4-H pig, Penelope. 1. What kind of diameter does this give me? 2. Penelope needs at least 700 square feet to, y know, do all of her pig stuff in. Are we good? A= π (R)2 700 = π (R) = (R) = R 29.8 feet = D 31
32 2. Pi. I bring home 90 feet of fencing for a circular pen to corral my 4-H pig, Penelope. 1. What kind of diameter does this give me? go the other direction on this one, ding dong. take the diameter from the last 2. Penelope needs at problem, least 700 halve square it, and plug feet it to, y know, do all of her in. pig stuff in. Are we good? C = π D 90 = π D 90 = (3.14) D 28.7 feet = D 32
33 3. Classwork pg. 333 // #1-14 What s wrong with this picture? 33
34 4. Break 5. Show and Tell 34
35 6. Circumference Word Problem Set Phileas Fogg and Around the World in Eighty Days If the diameter of the earth is 8000 miles, find the average speed in miles per hour Phileas Fogg needs to circumnavigate the earth about the equator in 80 days. If you add one foot of rope to the circumference of the earth how high off the ground could you pull it? 35
36 6. Circumference Word Problem Set (10 points) pg. 338 // #1, 4, 3, 6, 7 36
37 Diameter of the Earth is 8000 miles feet in a mile. A: feet Day Opener a) Stretch a cord tight across the equator. How long is it? Now add one mile to its length and stretch it into a new circle. How high off the ground will it be? b) Solve for x, y, and z. 128 z c) How much does a human head cost for science? x y 72 $500 37
38 Three-time Maverick s Surf Contest champion Darryl Flea Virostko of Santa Cruz... guesses \ most of the waves measured about 50 feet at the face, and about feet at the back. Santa Cruz Sentinel, December 6, How do you measure a wave?
39 Santa Cruz Sentinel, December 6,
40 2. Circumference / Radius / Diameter Chart radius diameter circumference area 5 inches 7 meters 7 feet 50 feet 2 19 hands 12 furlongs 9 parsecs Will the numbers ever decrease from left to right? Fractional radii. 40
41 2. Circumference / Radius / Diameter Chart a) A helicopter has three blades each measuring about 26 feet. What is the speed in feet per second at the tips of the blades when they are moving at 400 rpm? b) Two sides of a triangle are 24 cm and 36 cm. Write an inequality that represents the range of values for the third side. Answers here. 41
42 2. Circumference / Radius / Diameter Chart radius diameter circumference area 5 inches 10 inches 31.4 inches 78.5 inches meters 7 meters meters 38.5 meters feet 2.2 feet 7 feet 3.9 feet 2 4 feet 8 feet feet 50 feet hands 6.1 hands 19 hands 28.7 hands 2 6 furlongs 12 furlongs furlongs 113 furlongs 2 9 parsecs 18 parsecs parsecs parsecs 2 Answers here. 42
43 3. Notes
44 3. Notes
45 3. Notes Conjecture 38: Intersecting Chord Conjecture The measure of an angle formed by two intersecting chords is the average of the two intercepted arcs. 45
46 4. Classwork pg. 336 // #19, 20 b = 90, c = 42, d = 70, e = 48, f = 132, g = 52 ; AB = 45, CD = 105, P = 150/360 = 5/12 46
47 5. Break 6. Show and Tell 47
48 7. Basketball x \ 48
49 7. Basketball 150 x 75 \ 49
50 7. Basketball x60 \ 50
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52 7. Name That State Flag! Texas \ 52
53 7. Basketball x \ 53
54 7. Basketball 68 x 20 \ 54
55 7. Basketball 78 x51 \ 55
56 7. Name That State Flag! Arizona \ 56
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