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.2. Ability to use transformation notation (A➞A’➞A”).
8.G.1b. Angles are taken to angles of the same measure.
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.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.4.2. Ability to show that similar figures maintain shape but alter size through dilation (scale factor).
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.
Unit 2: Similarity, Proof, and Trigonometry
HSG-SRT.A. Understand similarity in terms of similarity transformations.
G.SRT.1a. Verify experimentally the properties of dilations given by a center and a scale factor – A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.SRT.1a.1. Ability to connect experiences with dilations and orientation to experiences with lines.
G.SRT.1b. Verify experimentally the properties of dilations given by a center and a scale factor – The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.1b.1. Ability to develop a hypothesis based on observations.
G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.2.1. Ability to make connections between the definition of similarity and the attributes of two given figures.
G.SRT.2.2. Ability to set up and use appropriate ratios and proportions.
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.