### Standard 8: Geometry from an Algebraic Perspective

In grades 9-12, the mathematics curriculum should include the continued study of geometry of two and three dimensions from an algebraic point of view so that students can:
• Translate between synthetic and coordinate representations

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• Identify congruent and similar figures using transformations

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• Deduce properties of figures using transformations and using coordinates

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• Analyze properties of Euclidean transformations and relate translations to vectors and similar figures using transformations
• 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.

Benchmarks 9C (The Mathematical World: Shapes)
It takes two numbers to locate a point on a map or any other flat surface. The numbers may be two perpendicular distances from a point, or an angle and a distance from a point.

Benchmarks 9C (The Mathematical World: Shapes)
Shapes on a sphere like the earth cannot be depicted on a flat surface without some distortion.

Benchmarks 9C (The Mathematical World: Shapes)