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Transcript
LaShawne R. Long Myles Guy Brown GSE Geometry 4.5 Week Cumulative Assessment Spring 2017 Understand and apply theorems about circles MGSE9-12.G.C.1 Understand that all circles are similar. MGSE9-12.G.C.2 Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. 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. Can you… 1. Identify the lines, line segments, and points associated with a circle. 2. Use the formulas associated with measures of arcs as well as angles to solve for particular quantities. MGSE9-12.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. MGSE9-12.G.C.4 Construct a tangent line from a point outside a given circle to the circle. Can you… 1. Utilize the characteristics of an inscribed quadrilateral in order to solve for particular quantities? 2. Use the characteristics of an inscribed right triangle in order to solve for angle measures? 3. Recognize the steps needed in order to construct a tangent line? Find arc lengths and areas of sectors of circles MGSE9-12.G.C.5 Derive 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. Can you… 1. Apply the formulas related to both arc length as well as sector area in order to determine particular values? 2. Relate the concept of radian measure to an exact answer with a relationship to the radius? Student Notes: