KEY STANDARDS ADDRESSED: MM2G3. Students will understand the properties of circles.


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1 KEY STANDARDS ADDRESSED:. Students will understand the properties of circles. a. Understand and use properties of chords, tangents, and secants an application of triangle similarity. b. Understand and use properties of central, inscribed, and related angles. c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector. d. Justify measurements and relationships in circles using geometric and algebraic properties. Aug 25 10:52 AM 1
2 Unit 3 key vocabulary *rate your knowledge of each term: 1. No clue! 2. Heard it before, but it is fuzzy. 3. I know this term well! radius chord tangent secant sector central angle inscribed angle area of circle diameter sphere surface area volume of spheres area of a sector arc length Aug 25 9:25 AM 2
3 Unit 3 Essential Questions Circles What are the basic parts of a circle? What is a circle? lesson powerpoints What are the properties of chords, tangents and secants in circles? What are the different types of angles (and their properties) formed by chords, tangents and secants? Circle arc length and sectors How can you use properties of circles to solve problems involving the length of an arc and the area of a sector? Spheres click to go to spheres How do you calculate surface area and volume of a sphere? How is the surface area and volume of a sphere altered when the radius is changed? lesson on arc length lesson on area of sectors Aug 25 9:31 AM 3
4 circle terms and parts day 1 tangents and circles day 1 CIRCLES arcs and chords day 1 special segments day 1 Mar 30 11:40 PM 4
5 classwork for each topic circle terms and parts tangents and circles arcs and chords special segments Apr 29 10:54 AM 5
6 Circles.notebook homework for each topic circle terms and parts tangents and circles arcs and chords special segments Apr 29 12:47 PM 6
7 Central and Inscribed Angles A central angle of a circle is an angle whose vertex is the center of the circle. Central Angle An inscribed angle is an angle in a circle, whose vertex is on the circle and whose sides contain chords of the circle. A D Inscribed Angle Intercepted Arc B is an inscribed angle. is the intercepted arc. A D B D A D A C E B C E B A D E C B Nov 9 10:02 AM 7
8 Examples A D 40 B D E C 40 A 240 B A C 270 B A 200 E B 100 D C E A C B D Nov 11 8:23 AM 8
9 A D C O E B F Nov 11 8:54 AM 9
10 Arcs in Circles An arc is part of a circle's circumference In circle O, the radius is 8, and the measure of minor arc AB is 110 degrees. Find the length of minor arc AB to the nearest integer. On line practice Homework Apr 30 9:18 AM 10
11 Area of a Circle Apr 30 9:06 AM 11
12 Area of a Sector What is the area of a semicircle? ½πr 2 What is the area of a quartercircle? ¼πr 2 What is the area of any section of a circle? πr 2 What if we are not given the angle? πr 2 Find the area of a sector with the central angle of 60º and a radius of 10. Express the answer to the nearest tenth. A = πr 2 A = π(10) 2 A = 52.4 Find the area of a sector with an arc length of 40 cm and a radius of 12 cm. A = π(12) 2 A = 240 sq. cm Sep 15 2:14 PM 12
13 A D x Area of a Sector E C A D Arc Length/Measure x C E Nov 30 9:01 AM 13
14 Segment of a Circle A segment of a circle is the region bounded by a chord and the arc. Segment Finding the area of a segment of a circle First, you must find the area of a the sector of the circle Second, find the area of the triangle Last, subtract the area of the triangle from the area of the sector to find the segment of the circle In other words: A segment = A sector A triangle Sep 15 3:06 PM 14
15 Find the area of a segment of a circle with a central angle of 120 degrees and a radius of 8. Express answer to nearest integer. Start by finding the area of the sector A = π(8) 2 A = π(64) A = Now, find the area of the triangle. Dropping the altitude forms a degree triangle. Using trig. (or the rules), find the altitude, which is 4, and the other leg, which is 4 3. A = ½ bh A = ½ (4 3)(4) A = We have two triangles, so we have to multiply that by 2. A = A segment = A sector A triangle A segment = A segment = 39.3 Sep 15 3:14 PM 15
16 Terms and definitions Review: A circle is the set of all points in a plane that are equidistant (the length of the radius) from a given point, the center, of the circle. A chord is a segment on the interior of a circle whose endpoints are on the circle. A diameter is a segment between two points on a circle, which passes through the center of the circle. An arc is a connected section of the circumference of a circle. An arc has a linear measurement, which is the portion of the circumference, and an arc has a degree measurement, which is a portion of the 360 degree circle. If a circle is divided into two unequal arcs, the shorter arc is called the minor arc and the longer arc is called the major arc. If a circle is divided into two equal arcs, each arc is called a semicircle. Draw a circle and label the parts listed above Mar 30 11:13 PM 16
17 MM2G4 A secant line is a line that intersects a circle at two points on the circle. A tangent line is a line that intersects the circle at exactly one point. A central angle of a circle is an angle whose vertex is the center of the circle. An inscribed angle is an angle in a circle, whose vertex is on the circle and whose sides contain chords of the circle. A sector of a circle is a region in the interior of the circle bounded by two radii and an Mar 30 11:21 PM 17
18 Teacher's test page: click on the link to open different versions of tests for unit 3 these were made using the mcdougal littel test generator version 1 version 2 part 2 Review items review #1 Review #2 May 12 2:52 PM 18
19 helpful websites %20Accelerate 20Math%20I%20Student%20Edition%20Unit%203%20Circles%20and%20Spheres.pdf interactive practice test bin/msgquiz.php4?isbn= &chapter=10&title=ct&&headerfile=x Mar 30 11:30 PM 19
20 Circle O with tangent. answers Apr 30 9:23 AM 20
21 Circle O with tangent MN answers Apr 30 9:20 AM 21
22 WATER WHEEL A circular water wheel is divided into 10 even parts by the spokes. If the radius of one of the spokes is 5 feet, what is the area of one of the sections? Apr 30 10:30 AM 22
23 angles within a circle segments in a circle Cyclic Quadrilaterals A cyclic quadrilateralis a four sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumf the circle. The opposite angles of such a quadrilateral add up to 180 degrees. In the circle O below, what are the measures of the numbered angles? quiz on circles May 5 10:08 PM 23
24 EXAMPLE Find the area of a sector with a central angle of 60 degrees and a radius of 10. Express answer to the nearest tenth. Apr 30 9:10 AM 24
25 Apr 30 9:23 AM 25
26 KEY STANDARDS ADDRESSED: MM2G4. Students will find and compare the measures of spheres. a. Use and apply surface area and volume of a sphere. b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Jul 21 11:42 AM 26
27 MM2G4 Spheres the basics powerpoint on changing radius Spheres HW Spheres classwork On line practice with spheres Apr 29 12:44 PM 27
28 Attachments circle terms.ppt circle properties and HW.pdf tangents.ppt angle formulas.ppt circle tangents and theorems.ppt arcs and chords.ppt special segments.ppt spheres.ppt angle formulas HW.pdf arcs and chords classwork.pdf arcs and chords HW.pdf circle parts Classwork.pdf cirlce parts HW.pdf special segments classwork.pdf special segments HW.pdf spheres classwork.pdf spheres HW.pdf tangents classwork.pdf tangents HW.pdf areas of sectors and segments HW.pdf AreaSectorSegment912quiz.pdf circles+test.tst unit 3 test circles.tst unit 3 part 2 test.tst circles review sheet.tst unit 3 part 2 review.tst MA1G5b spheres.ppt unit 3 overview page.pdf Area of a Sector.ppt practice on arc length and area of sectors.pdf
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