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# Mathematics Curriculum Framework - November 2000

## Learning Standards

 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Specify locations and describe spatial relationships using coordinate geometry and other representational systems Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems

#### Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

 10.G.1 Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry. 10.G.2 Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. 10.G.3 Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. 10.G.4 Apply congruence and similarity correspondences (e.g., ΔABC ΔXYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification. 10.G.5 Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. 10.G.6 Use the properties of special triangles (e.g., isosceles, equilateral, 30°-60°-90ยบ, 45°-45°-90°) to solve problems. 10.G.7 Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems. 10.G.8 Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation. 10.G.9 Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems. 10.G.10 Demonstrate the ability to visualize solid objects and recognize their projections and cross sections. 10.G.11 Use vertex-edge graphs to model and solve problems.

#### Exploratory Concepts and Skills for Grades 9-10 and Single-Subject Courses

• Apply properties of chords, tangents, and secants to solve problems.
• Use deduction to establish the validity of geometric conjectures and to prove theorems in Euclidean geometry.

Geometry