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Transcript

Geometry Curriculum Paterson Charter School for Science and Technology 2014-2015 Unit 3 Summary: Circles Essential Questions Big Ideas The length of part of a circle’s circumference can be found by relating it to a central angle in the circle. The area of a circle can be found when the circle’s radius is known. The area of parts of a circle formed by radii and an arc can be found when the circle’s radius and the arc measures are known. Information about congruent parts of a circle (or congruent circles) can be used to find information about other parts of the circle (or circles). Angles formed by intersecting lines have a special relationship to the arcs the intersecting lines intercept. Geometry Curriculum Unit 4:Circles Unit 3 Summary: Circles Learning Outcomes (CCSS) G.C.1 Prove that all circles are similar. G.C.2 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. G.C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle. Find arc lengths and areas of sectors of circles G.C.5Derive using similarity the fact that the length of the arc intercepted by an angle 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. Local Standards (LS) #24-25 are taught in this unit. 51. Prove that all circles are similar. 52. Find the circumference, measure of central angles and arcs of a circle. 53. 54. 55. 56. 57. 58. 59. Use congruent chords, arcs, central angles and perpendicular bisectors to chords. Identify and describe relationships among inscribed angles, radii and chords. Construct the inscribed and circumscribed circles of a triangle. Prove properties of angles for a quadrilateral inscribed in a circle. Derive using similarity that the fact that the length of the arc intercepted by an angle is proportional to the radius. Define the radian measure of the angle as the constant of proportionality. Derive the formula for area of sector. Geometry Curriculum Unit 4: Circles Unit 3 Summary: Circles Prior Knowledge Expected Basic parts of circle. Assessment Summary 1. Mid Unit Assessment (LS#51-54) 2. End-of-Unit Assessment (LS #55-59) (Scope and Sequence on the next page) Geometry Curriculum Unit 4:Circles Unit 1 Scope and Sequence: Number System Fluency Periods* CCSS LS Student Friendly Language Resources Textbook Pearson 10-6 Links 1 G.C.1 S51 Prove that all circles are similar. Other Find the circumference, measure of central angles and arcs of 1 G.C.1 S52 Assessment Skill Check 51 Textbook Pearson 10-6 Links a circle. Other Assessment Skill Check 52 Textbook 1 G.C.1 S53 Use congruent chords, arcs, central angles and perpendicular bisectors to chords. Links Other 1 G.C.2 S55 Identify and describe relationships among inscribed angles, radii and chords. Assessment Skill Check 53 Textbook Pearson 10-6, Concept Byte 106, 12-2, 12-3 Links Geometry Curriculum Unit 4: Circles Other 1 G.C.3 S56 Construct the inscribed and circumscribed circles of a triangle. Assessment Skill Check 55 Textbook Pearson 5-3 Links Other 1 G.C.3 S57 Prove properties of angles for a quadrilateral inscribed in a circle. Assessment Skill Check 56 Textbook Pearson 12-3 Links Other Assessment Textbook Skill Check 57 Pearson 10-6, 10-7 Links 1 G.C.5 S58 Define the radian measure of the angle as the constant of proportionality. Other 1 G.C.5 S59 Derive the formula for area of sector. Assessment Skill Check 58 Textbook Pearson 10-6, 10-7 Links Other Geometry Curriculum Unit 4:Circles Assessment Geometry Curriculum Skill Check 59 Unit 4: Circles