Maryland College and Career-Ready Standards
MD.MA.8.G. Geometry (G)
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.1. Verify experimentally the properties of rotations, reflections, and translations.
8.G.1a. Lines are taken to lines, and line segments to line segments of the same length.
8.G.1a.1. Ability to conduct experiments which show that rotations, reflections, and translations of lines and line segments are rigid.
8.G.1a.2. Ability to use transformation notation (A➞A’➞A”).
8.G.1b. Angles are taken to angles of the same measure.
8.G.1b.1. Ability to conduct experiments which show that rotations, reflections, and translations of angles are rigid.
8.G.1b.2. Ability to use transformation notation (∠A➞∠A’➞∠A”).
8.G.1c. Parallel lines are taken to parallel lines.
8.G.1c.1. Ability to conduct experiments which show that rotations, reflections, and translations of parallel lines are rigid.
8.G.1c.2. Ability to use transformation notation (A➞A’➞A”).
8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.2.1. Ability to use a sequence of transformations and map one figure to a second figure to show congruency.
8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.4.3. Ability to demonstrate that congruency is a special case of similarity (scale factor of 1).
Unit 1: Congruence, Proof, and Constructions
HSG-CO.A. Experiment with transformations in the plane.
G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.1.1. Ability to use mathematical vocabulary accurately.
G.CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch.
G.CO.2.1. Ability to see parallels between function transformations (F.BF.3) and geometric transformations.
G.CO.2.2. Knowledge that rigid transformations preserve the size and shape of a figure.
G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.3.1. Ability to use appropriate vocabulary to describe rotations and reflections.
G.CO.3.2. Ability to use the characteristics of a figure to determine and then describe what happens to the figure as it is rotated (such as axis of symmetry, congruent angles or sides…).
G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.4.1. Ability to construct a definition for each term based upon a synthesis of experiences.
HSG-CO.B. Understand congruence in terms of rigid motions.
G.CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.6.1. Ability to recognize the effects of rigid motion on orientation and location of a figure.
G.CO.6.2. Ability to use rigid motions to map one figure onto another.
G.CO.6.3. Ability to use the definition of congruence as a test to see if two figures are congruent.
G.CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.7.1. Knowledge of vocabulary corresponding parts and the connection to the given triangles.
G.CO.7.2. Ability to identify the corresponding parts of two triangles.
Unit 2: Similarity, Proof, and Trigonometry
HSG-MG.A. Apply geometric concepts in modeling situations.
G.MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
G.MG.1.1. See the skills and knowledge that are stated in the Standard.