Geo+Unit+6

1. Make sense of problems and perseveres in solving them. 2. Reasons abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity and repeated reasoning. || Remembering Understanding Applying Analyzing Evaluating Creating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard(s)**===
 * 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.3**. Construct 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.
 * 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.
 * G-GPE.1.** 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.
 * G-GPE.2.** Derive the equation of a parabola given a focus and directrix. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**===
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**===

**I can...**

 * Prove all circles are similar
 * Define and use properties of tangent lines, inscribed angles, radii, central angles, circumscribed angles and chords
 * Construct inscribed circles of a triangle
 * Construct circumscribed circles of a triangle
 * Prove properties of angles in a quadrilateral inscribed in a circle
 * Construct a tangent line to a circle
 * Prove the fact that the length of an arc is proportional to the radius
 * Find the arc length of a circle
 * Derive the formula for the area of a sector
 * Find the area of a sector in a circle
 * Use the Pythagorean theorem to derive the equation of a circles given the center and radius
 * Complete the square to find the center and radius of a circle
 * Derive the equation of a parabola given a focus and directrix
 * Identify the vertex, focus, directrix, and axis of symmetry of a parabola

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Essential Vocabulary**
radius, chord, central angle, inscribed angle, circumscribed angle, diameter, tangent line, area of a sector, arc length, conic sections, parabola, focus, directrix

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**===

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**===

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===