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.
INTERPRETATION OF OBJECTIVE - G.C.A.2
This objective is huge. Basically this objective covers all of the typical covered circle objectives. While not everything is listed directly this objective is about covering the essential relationships found in the circle concerning angles, arcs and chords.
(1) The student will be able to determine angle values for all angles formed in the exterior, interior and on the circle.
(2) The student will be able to apply knowledge of arcs, angles and chords to solve circle related problems.
(3) The student will be able to determine lengths of intersecting chords and secants.
THE BIG IDEA
The circle has many specialized properties and relationships and the knowledge of them help us to determine more relationships in the circle. Circle geometry is really not very important in the big picture - much of the relationships don't translate into other areas.
TRAPS & PITFALLS
The interior angle formula and the external angle formula are quite simply when both arcs are provided but if one of them is missing the problem seems to get much more difficult. I have the students practice more of these.
The other area is the length relationships. They are not as simple to use or remember as the angle relationships. The length relationships often involve more algebraic operations to solve and sometimes even bring out a quadratic equation - this causes great grief for the students... imagine that doing quadratic equations in geometry.
Circle geometry is lightly related the other units. Knowing ratios and proportional is very helpful for some of the relationships.
We will transition from general relationships to those found in a coordinate setting.
MY REFLECTIONS (over line l)
My reflection on this area each year is that I expect students to get it because I view the materials as quite simple but they often don't just get it. I think they find the material hard to remember or distinguish and they often mix up relationships. The math is very simple it is usually just the correct or incorrect use of certain relationships. I have found doing some summary sheets or reference sheets as we progress to be very helpful. I don't allow them to use them on the quiz but in preparation for the quiz it seems to be quite useful!