### Standard 7: Geometry from a Synthetic Perspective

In grades 9-12, the mathematics curriculum should include the continued study of geometry of two and three dimensions so that students can:
• Interpret and draw three-dimensional objects
• Benchmarks 9C (The Mathematical World: Shapes)
Many objects can be described in terms of simple plane figures and solids. Shapes can be compared in terms of concepts such as parallel and perpendicular, congruence, similarity, and symmetry. Symmetry can be found by reflection, turns, or slides.

• Represent problem situations with geometric models and apply properties of figures
• Benchmarks 9C (The Mathematical World: Shapes)
Different ways to map a curved surface (like the earth’s) onto a flat surface have different advantages.

Benchmarks 12D (Habits of Mind: Communication Skills)
Make and interpret scale drawings.

Benchmarks 9C page 225 (The Mathematical World: Shapes)
Distances and angles that are inconvenient to measure directly can be found from measurable distances and angles using scale drawings or formulas.

• Classify figures in terms of congruence and similarity and apply these relationships
• Benchmarks 12D (Habits of Mind: Communication Skills)