G.C.2 Clarifications

[dward]

The following paragraph which is describing what students should learn in Unit 5 of Geometry appears   on page 27 and again on page 34 of Appendix A to the Common Core.

Critical Area 5: In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations, which relates back to work done in the first course, to determine intersections between lines and circles or parabolas and between two circles.

The portion of this paragraph that is not bolded  is what I was hoping to have clarified.  I assume that these statements apply to standard G.C.2 (the language of G.C.2 is shown below ) because I can see no other standard to which the statement shown in the non bolded type  in the Critical Area 5 description might apply.  

 

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.

 

Is it  the expectation that the theorems described at the following link be covered by the Common Core High School Geometry? The language in the Critical Area 5 paragraph makes me believe that the theorems should be covered but the language in the standard does not make this clear.

http://www.regentsprep.org/Regents/math/geometry/GP14/CircleSegments.htm

 

Thanks for your reply

[Bill McCallum]

The interpretation in Appendix A is an extension of the standard, certainly not an unreasonable one, but it would be hard to argue that the standards require the theorems you link to, since they don’t list them in the things to be included, and the standard, although it mentions chords, does not mention segments on chords. I think this is a difference between what a well-rounded implementation of the standards might include, and what might appear on an assessment. The standards avoid comprehensive lists, while providing an overall structure in which extensions can find a natural home.

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