See the skills and knowledge that are stated in the them. Standard. Reason abstractly and G.C.2 Identify and describe relationships among inscribed quantitatively. angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on Construct viable a diameter are right angles; the radius of a circle is arguments and perpendicular to the tangent where the radius critique the intersects the circle. reasoning of others. Essential Skills and Knowledge Model with See the skills and knowledge that are stated in the mathematics. Standard. G.C.3 Construct the inscribed and circumscribed circles of a Use appropriate triangle, and prove properties of angles for a quadrilateral tools inscribed in a circle. strategically. Essential Skills and Knowledge Ability to use concurrence of perpendicular bisectors Attend to precision. and angle bisectors for the basis of the construction Look for and make G.C.4 (+) Construct a tangent line from a point outside a given use of structure. circle to the circle. Look for and express Essential Skills and Knowledge regularity in See the skills and knowledge that are stated in the repeated Standard. reasoning. G.C.5 Derive using similarity the fact that the length of the arc Make sense of intercepted by an angle is proportional to the radius, and define problems and the radian measure of the angle as the constant of persevere in solving proportionality; derive the formula for the area of a sector. them. Find arc lengths and Note: Emphasize the similarity of all circles. Note that by Reason abstractly areas of sectors of similarity of sectors with the same central angle, arc lengths are circles. and proportional to the radius. Use this as a basis for introducing quantitatively. radian as a unit of measure. It is not intended that it be applied to the development of circular Trigonometry in this course. Construct viable Essential Skills and Knowledge arguments and critique the See the skills and knowledge that are stated in the reasoning of others.
See the skills and knowledge that are stated in the Standard. 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. Essential Skills and Knowledge See the skills and knowledge that are stated in the Standard. G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Essential Skills and Knowledge Ability to use concurrence of perpendicular bisectors and angle bisectors for the basis of the construction G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle. Essential Skills and Knowledge See the skills and knowledge that are stated in the Standard. them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Find arc lengths and areas of sectors of circles. 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. Note: Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular Trigonometry in this course. Essential Skills and Knowledge See the skills and knowledge that are stated in the Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others.
GeometryFramework.docx