NC.M2.G-CO

NC.M2.G-CO

NC.M2.G-CO.10Prove theorems about triangles and use them to prove relationships in geometric figures including:NC.M2.G-CO.10aThe sum of the measures of the interior angles of a triangle is 180.NC.M2.G-CO.10bAn exterior angle of a triangle is equal to the sum of its remote interior angles.NC.M2.G-CO.10cThe base angles of an isosceles triangle are congruent.NC.M2.G-CO.10dThe segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length.NC.M2.G-CO.2Experiment with transformations in the plane.NC.M2.G-CO.2aRepresent transformations in the plane.NC.M2.G-CO.2bCompare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both distance and angle measure (e.g. stretches, dilations).NC.M2.G-CO.2cUnderstand that rigid motions produce congruent figures while dilations produce similar figures.NC.M2.G-CO.3Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry i.e., actions that carry the figure onto itself. Identify center and angle(s) of rotation symmetry. Identify line(s) of reflection symmetry.NC.M2.G-CO.4Verify experimentally properties of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.NC.M2.G-CO.5Given a geometric figure and a rigid motion, find the image of the figure. Given a geometric figure and its image, specify a rigid motion or sequence of rigid motions that will transform the pre-image to its image.NC.M2.G-CO.6Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other.NC.M2.G-CO.7Use the properties 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.NC.M2.G-CO.8Use congruence in terms of rigid motion. Justify the ASA, SAS, and SSS criteria for triangle congruence. Use criteria for triangle congruence (ASA, SAS, SSS, HL) to determine whether two triangles are congruent.NC.M2.G-CO.9Prove theorems about lines and angles and use them to prove relationships in geometric figures including:NC.M2.G-CO.9aVertical angles are congruent.NC.M2.G-CO.9bWhen a transversal crosses parallel lines, alternate interior angles are congruent.NC.M2.G-CO.9cWhen a transversal crosses parallel lines, corresponding angles are congruent.NC.M2.G-CO.9dPoints are on a perpendicular bisector of a line segment if and only if they are equidistant from the endpoints of the segment.NC.M2.G-CO.9eUse congruent triangles to justify why the bisector of an angle is equidistant from the sides of the angle.
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