G.C.A.1 -- Prove that all circles are similar.


G.C.A.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.A.3 --Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle

 

G.C.A.4 -- Construct a tangent line from a point outside a given circle to the circle.

 

G.C.B.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.

 


   

(1)To continue our connectivity to transformation we begin talking about the similarity of circles.  This idea is essential to understanding radians later.  We also hit the basic circle terms and relations.

(2)In week 2 we start dealing with tangent lines, chord properties and inscribed angles.

(3) In week 3 we look at the other angles that can be formed inside, on and out of the circle.  We also look at the length relationship found with chords and secants.

(4)Continuing the theme of constructions throughout the year we look at the construction of the circle.  The final theme of the unit is radian measure.  We look at what a radian is and how to understand its values.

(5)Finally we look at formulas that are greatly simplified when in radians and their applications.  This week we would also introduce the equation of a circle.