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# Mathematics Curriculum Framework - November 2000

## Learning Standards by Strand

 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:

 8.G.1 Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons. 8.G.2 Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. 8.G.3 Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. 8.G.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems. 8.G.5 Use a straight-edge, compass, or other tools to formulate and test conjectures, and to draw geometric figures. 8.G.6 Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations. 8.G.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces. 8.G.8 Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.

#### Exploratory Concepts and Skills for Grades 7-8 and Single-Subject Courses

• Investigate trigonometric ratios in right triangles.
• Investigate right triangle relationships, such as those in 45°-45°-90° and 30°-60°-90° triangles.
• Explore proofs of the Pythagorean theorem.

Geometry