Volume problem The diameter of a sphere is 12ft What is the volume to the nearest tenth?
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Transcript of Volume problem The diameter of a sphere is 12ft What is the volume to the nearest tenth?
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Volume problem The diameter of a sphere is 12ft What is the volume to the nearest tenth?
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Where do you see arcs and angles together?
Basketball Soccer Think of the arc around the net/goal What shot is easier:
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Circles have arcs Congruent arcs have congruent central angles Chords – congruent chords are equidistant from
the center and have congruent central angles Pg. 774 diameter and chords, will be
perpendicular (perpendicular bisector) http://www.youtube.com/user/EducatorVids?v=I
8kg3hWXjho&feature=pyv&ad=8603464868&kw=arcs
Angles with circles equation of circle
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Inscribed angle Central angle
Measure of the angle is ½ the arc
Pg. 781 got it #1 a and b
Pg. 782 - 787
Starts from the center of the circle
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equation of circle problems Pg. 801 – 802 (12, 16, 18, 22, 24, 26, 34,
38, 42, 54) discuss problems from 12-1, 12-2, & 12-3
problems Pg. 785 #24 Pg. 787 #40
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What is difference between inscribed and central angle?
How do you find the equation of a circle within a coordinate plane?
Homework: have a quarter Tuesday
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circle problem 1) write the standard equation of a circle
with center (2, -8) and r = 9
2) write the standard equation of the circle with center ( -2, 6) and the circle passes through point ( - 2, 10)
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do you see parabolas in places, if so where? What is the probability you see one on a
daily basis Carowinds Basketball court St. Louis
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Finish arcs, angles, discuss parabolas (conic sections),
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Inscribed angle Central angle
Measure of the angle is ½ the arc
Pg. 781 got it #1 a and b
Pg. 782 – 787 Pg. 785 #24 Pg. 787 #40
Starts from the center of the circle
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Lines of symmetry Domain Range Equation of a parabola, Focus Directrix http://www.mathsisfun.com/geometry/parab
ola.html Conic section – simply the intersection of a
plane and a cone
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http://www.mathwords.com/p/parabola.htm The focus of a parabola is a fixed point on
the interior of a parabola used in the formal definition of the curve.
Locus◦ A word for a set of points that forms a
geometric figure or graph. For example, a circle can be defined as the locus of points that are all the same distance from a given point.
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Directrix of a Parabola◦ A line perpendicular to the axis of symmetry used
in the definition of a parabola. The parabola is the curve formed from all
the points (x, y) that are equidistant from the directrix and the focus.
A parabola must satisfy the conditions listed above, and a parabola always has a quadratic equation.
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The "general" form of a parabola's equation is the one you're used to, y = ax2 + bx + c — unless the quadratic is "sideways", in which case the equation will look something like x = ay2 + by + c.
The important difference in the two equations is in which variable is squared: for regular (vertical) parabolas, the x part is squared; for sideways (horizontal) parabolas, the y part is squared.
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The "vertex" form of a parabola with its vertex at (h, k) is:
regular: y = a(x – h)2 + k sideways: x = a(y – k)2 + h
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conic sections Parabolas
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arc circle problems: pg. 784 #6, 10, 12, 14, 16, and 18
parabola problem (today or Wednesday)
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equation of circle problems Pg. 801 – 802 (12, 16, 18, 22, 24, 26, 34,
38, 42, 54) discuss problems from 12-1, 12-2, & 12-3
problems
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dart boards deal with concentric circles & inscribed angles
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Darts Carnival games Soccer nets Basketball nets Activity: concentric circles on the white
board, what is the probability you get a bull’s eye
Activity: coin toss – if you flip a coin 20 times, then what is the ratio of heads to tails
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How are central angles and inscribed angles different and how are they similar?
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angle problem practice1)pg. 181 #6, 8, 102)Pg. 181 #16
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review for tomorrow’s test and BIG review for common exam
If you find yourself finished with all the problems, correctly, then complete the following:
Define: experimental probability, simulation, sample space, and theoretical probability AND practice parabola stuff using ipad
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Explain a math concept that we have discussed and been tested on; assume you are explaining it to a student who will take Geometry next year.
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Geometric Proability pg. 668
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Prove circles similar
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circle angle problem:1)Radius is 12, what is half the length of the
chord?
8
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Tangent linesA) With inscribed shapes◦Thm. 12-3; if 2 tangent lines that share a common endpoint, then the 2 segments are congruent◦Pg. 766B) Lines & quadrilaterals
a tangent line and a radius create a 90 degree angle (p. 762 & 763)
a quadrilateral = 360 degrees
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Section 12-3 Circle inscribed in a polygon p. 767 #19 P.769 #32
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Central angles◦ The central angle of a circle is the angle based
at the circle's center. ◦ In other words, the vertex of the angle must be
at the center of the circle. ◦ A central angle is formed by two radii that start
at the center and intersect the circle itself.◦ Central Angle = Intercepted Arc◦ http://www.regentsprep.org/Regents/math/geometry/
GP15/CircleAngles.htm◦ http://www.icoachmath.com/math_dictionary/
Central_Angle.html
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Do you remember formula? Angle = ½ arc
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Is there an activity that involves circles, but also involves probability?
darts
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Chapter 12 tangent lines, Pythagorean thm, and arcs
you must complete today, due before you leave
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How is your brain improving because you are learning math? Give an example