GEO-G.CO

Geometry – Congruence

GEO-G.CO.1Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.GEO-G.CO.10Prove and apply theorems about triangles.GEO-G.CO.11Prove and apply theorems about parallelograms.GEO-G.CO.12Make, justify, and apply formal geometric constructions.GEO-G.CO.13Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.GEO-G.CO.2Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.GEO-G.CO.3Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that carry the polygon onto itself.GEO-G.CO.4Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.GEO-G.CO.5Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.GEO-G.CO.6Use 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.GEO-G.CO.7Use 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.GEO-G.CO.8Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.GEO-G.CO.9Prove and apply theorems about lines and angles.
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