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The learner will…
- Recognize that all circles are similar.
(I can prove that all circles are similar.)
- 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, and properties of angles for a quadrilateral inscribed in a circle.
(I can identify central angles, inscribed angles, circumscribed angles, diameters, radii, chords, and tangents. I can describe the relationship between a central angle and its intercepted arc. Page 2 of 4 I can describe the relationship between an inscribed angle and its intercepted arc. I can describe the relationship between a circumscribed angle and its intercepted arcs. I can describe the relationship between two secants, a secant and a tangent or two tangents in relation to the intercepted circle. I can verify that inscribed angles on a diameter are right angles. I can verify that the radius of a circle is perpendicular to the tangent where the radius intersects the circle.)
-Construct the in-center and circumcenter of a triangle and use their properties to solve problems in context
(I can construct the inscribed circle whose center is the point of intersection of the angle bisectors (incenter). I can prove that the opposite angles in an inscribed quadrilateral are supplementary. I can construct the circumscribed circle whose center is the point of intersection of the perpendicular bisectors (circumcenter).)
-Know the formula and find the area of a sector of a circle in a real-world content.
(I can use the formula for the area of a sector. I can find the area of a sector.)
-Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.
(I can use the Pythagorean Theorem to derive the equation of a circle, given the center and radius. I can complete the square to find the center and radius of a circle when given an equation of a circle.)
Honors Addendum
Embed the Honors Addendum within the regular Scope & Sequence.
-Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
-Construct a tangent line from a point outside a given circle to the circle.
-Derive the equation of a parabola given a focus and directrix.
-Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
(I can state that if, two solid figures have the same total height and their cross-sectional areas are identical at every level, the figures have the same volume (Cavalieri’s Principle). I can construct a tangent line from a point outside a given circle to the circle. I can derive the equation of a parabola given a focus and directrix. I can derive the equation of an ellipse given the foci, noting that the sum of the distances from the foci to any fixed point on the ellipse is constant. I can identify the major and minor axis of an ellipse. I can derive the equation of a hyperbola given the foci, noting that the absolute value of the differences of the distances from the foci to a point on the hyperbola is constant. I can identify the vertices, center, transverse axis, conjugate axis, and asymptotes of a hyperbola. )
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