G.CO

Congruence

G.CO.1(9/10) Verify experimentally (for example, using patty paper or geometry software) the properties of rotations, reflections, translations, and symmetry:G.CO.10(9/10) Construct arguments about parallelograms using theorems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. (Building upon prior knowledge in elementary and middle school.)G.CO.11(9/10) Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.G.CO.12(+) Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.G.CO.1a(9/10) Lines are taken to lines, and line segments to line segments of the same length.G.CO.1b(9/10) Angles are taken to angles of the same measure.G.CO.1c(9/10) Parallel lines are taken to parallel lines.G.CO.1d(9/10) Identify any line and/or rotational symmetry within a figure.G.CO.2(9/10) Recognize transformations as functions that take points in the plane as inputs and give other points as outputs and describe the effect of translations, rotations, and reflections on two-dimensional figures. For example, (x,y) maps to (x + 3, y - 5); reflecting triangle ABC(input) across the line of reflection maps the triangle to exactly one location, A'B'C'(output).G.CO.3(9/10) Given two congruent figures, describe a sequence of rigid motions that exhibits the congruence (isometry) between them using coordinates and the non-coordinate plane.G.CO.4(9/10) 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.5(+) Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.G.CO.6(+) Demonstrate triangle congruence using rigid motion (ASA, SAS, and SSS).G.CO.7(9/10) Construct arguments about lines and angles using theorems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. (Building upon standard in 8th grade Geometry.)G.CO.8(9/10) Construct arguments about the relationships within one triangle using theorems. Theorems include: measures of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point; angle sum and exterior angle of triangles.G.CO.9(9/10) Construct arguments about the relationships between two triangles using theorems. Theorems include: SSS, SAS, ASA, AAS, and HL.
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