1. 2009 MATHEMATICS STANDARDS OF LEARNING TRAINING INSTITUTES
GEOMETRY
Virginia Department of Education

2. Major Changes Content moved to grades 6-8 Content added
Geometry
Major Changes
Content moved to grades 6-8
Complementary, supplementary, and vertical angles
Content added
Equation of circle given coordinates of center and point on circle
Reorganization of reporting categories
Course designed for students who have successfully completed algebra I
Course includes properties of geometric figures, trigonometric relationships, and reasoning to justify conclusions.
Methods of justifications include paragraph proofs, two-column proofs, indirect proofs, coordinate proofs, algebraic methods, and verbal arguments.
How geometry grows from k-7 to high school in complexity

3. Reporting Category Changes
Geometry
Reporting Category Changes
Old reporting categories
Lines and Angles
Triangles and Logic
Polygons and Circles
Three-Dimensional Figures
Coordinate Relations and Transformations
New reporting categories
Reasoning, Lines, and Transformation
Triangles
Polygons and Circles
Three-Dimensional Figures
Lines, angles, triangles, logic, coordinate relations, and transformations split into two new categories to make reporting for some sols easier.

4. Geometry Reporting Category Topics
Reasoning, Lines, and Transformation
Logic, angle relationships with parallel lines, coordinate geometry, constructions
Triangles
Characteristics, congruence, similarity, Pythagorean Theorem and right triangle geometry
Polygons and Circles
Properties of quadrilaterals, angles of polygons, properties of circles, equation of a circle
Three-Dimensional Figures
Surface area, volume, dimensional changes affecting volume and surface area

5. Geometry
Standard G.12
The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.
From the proposed Curriculum Framework
Standard form for the equation of a circle is
where the coordinates of the center of the circle are (h, k) and r is the length of the radius.

6. Proposed Curriculum Framework G.12
Geometry
Proposed Curriculum Framework G.12
Identify the center, radius, and diameter of a circle from a given standard equation.
Use the distance formula to find the radius of a circle.
Given the coordinates of the center and radius of the circle, identify a point on the circle.
Given the equation of a circle in standard form, identify the coordinates of the center and find the radius of the circle.
Given the coordinates of the endpoints of a diameter, find the equation of the circle.
Given the coordinates of the center and a point on the circle, find the equation of the circle.

7. Sample Activity for G.12 Geometry
Given the endpoints of the diameter of a circle,
(4, -2) and (6,8):
1. Find the center of the circle.
2. Find the radius or the circle.
3. Write the equation of the circle in standard form.