A2. Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:
a. Determine when one set of figures is a subset of another; e.g., all squares are rectangles.
b. Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent.

A3. Use and demonstrate understanding of the properties of triangles.
For example:
a. Use Pythagorean Theorem to solve problems involving right
triangles.
b. Use triangle angle sum relationships to solve problems.

A8. Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).

Characteristics andPropertiesA1. Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures.

A2. Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:

a. Determine when one set of figures is a subset of another; e.g., all squares are rectangles.

b. Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent.

A3. Use and demonstrate understanding of the properties of triangles.

For example:

a. Use Pythagorean Theorem to solve problems involving right

triangles.

b. Use triangle angle sum relationships to solve problems.

A4. Determine necessary conditions for congruence of triangles.

A5. Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures. Spatial Relationships

A6. Determine and use scale factors for similar figures to solve problems using proportional reasoning.

Transformations andSymmetryA7. Identify the line and rotation symmetries of two-dimensional figures to solve problems.

A8. Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).

Visualization andGeometricModelsA9. Draw representations of three-dimensional geometric objects from different views.