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EAST ALLEN COUNTY SCHOOLS Bundle 7 Geometry Circles Big Idea: Things that go around Enduring Understandings Essential Questions Special lines, angles, and arcs of a circle have many special relationships. Properties fo right triangles are used to derive equations for circles and parabolas. Constructions are used to determine many properties of a circle. How can the coordinate plane be used to derive the equation of a circle and a parabola? What is the relationship between angles and arcs formed by chords, secants, and tangents? How can constructions be used to inscribe and circumscribe a circle in a triangle? CC/Learning Targets G.GPE.1 G.GPE.2 G.C.2 G.C.3 G.C.4 G.C.5 Core Vocabulary Links to Technology chord secant tangent to a circle Bundle Performance Task(s) The students will create a new clock design of the Floral Clock in Niagara Falls, Canada, given the circumference. Students need to find the lengths of the hands of the clock, the area of each of the 12 sectors in which the letters to spell out Niagara Parks will be placed, and the final design of the clock face using geometry software or hand drawn visual to present to the class. The final product will be displayed throughout the school. Geometry Bundle 7 Quarter 4 Mar.-Apr. Geometry CC/Learning Targets G.GPE.1 (G.6.8a,c) G.GPE.2 G.C.2 (G.6.1a) (G.6.2a-b) (G.6.4c) (G.6.5a-c) G.C.3 (G.6.1b) (G.6.4c) (G.8.9a) G.C.4 (G.6.4c) (G.8.9a) Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Derive the equation of a parabola given a focus and directrix. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Construct a tangent line from a point outside a given circle to the circle. Bundle 7 Resource of Ideas -Completing the square: Circle Equations -Equation of a circle -Prentice Hall Mathematics Lessons 11.5 -iBook Prentice Hall Geometry Lesson 12.5 -Equation of a Parabola -iBook Prentice Hall Geometry Lesson 12.5 -Angles in a circle -Segments of a circle -Prentice Hall Mathematics Lessons 5.3, 7.6, 7.7, 11.1-11.5 -iBook Prentice Hall Geometry Lessons 10.6, 12.1-12.4 -Construct inscribed circle in a triangle -Prentice Hall Mathematics Lessons 5.3 -iBook Prentice Hall Geometry Lessons 5.3, 12.3 -Construct tangent to a circle from external point -Prentice Hall Mathematics Lessons 5.3 -iBook Prentice Hall Geometry Lesson 12.3 Evidence of Learning -Class discussion -Graphing -White Board -Worksheet -Class Discussion -Graphing -White Board -Journal -Flip Chart -Flash Cards -Nearpod -Homework -Quiz/test -Construction -White Board -Patty Paper -Homework -Construction -White Board -Patty Paper -Homework Geometry G.C.5 (G.6.7d) Bundle 7 Derive using similarity the fact that the length of the arc intercepted by an angle measured in radians is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Correlating CC/Learning Targets G.CO.1 G.CO.2 G.CO.4 G.CO.6 G.CO.9 G.CO.13 G.GMD.1 G.GMD.3 G.SRT.4 G.SRT.5 G.SRT.6 G.SRT.7 G.SRT.8 G.GPE.4 G.C.1 -Area of sector -Radian measure -Derive formula for area of a sector -Class Discussion -Group Work -Homework -Quiz/Test -Prentice Hall Mathematics Lessons 7.7 -iBook Prentice Hall Geometry Lessons 10.6, 10.7 Teacher Notes All embeded apps included in this curriculum are free.