2009 MATHEMATICS STANDARDS OF LEARNING TRAINING INSTITUTES

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

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

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.

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

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.

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.

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.