Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Describe and use the concepts of congruence, similarity and symmetry to solve problems.
Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.
Represent and model transformations in a coordinate plane and describe the results.
Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
Grade Level Indicators (Grade 6)
Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.
Grade Level Indicators (Grade 7)
Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).
Grade Level Indicators (Grade 8)
Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.
Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations.
Grade Level Indicators (Grade 10)
Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; and
d. test a conjecture using basic constructions made with a compass and straightedge or technology.
Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable.
Principles and Standards for School Mathematics
Apply transformations and use symmetry to analyze mathematical situations
describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling;
examine the congruence, similarity, and line or rotational symmetry of objects using transformations.
understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;
use various representations to help understand the effects of simple transformations and their compositions.