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STANDARDS

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US-SC

Math

South Carolina Math

Geometry: Congruence

G.GCO.1

Fully covered
Define angle, perpendicular line, parallel line, line segment, ray, circle, and skew in terms of the undefined notions of point, line, and plane. Use geometric figures to represent and describe real-world objects.

G.GCO.2

Mostly covered
Represent translations, reflections, rotations, and dilations of objects in the plane by using paper folding, sketches, coordinates, function notation, and dynamic geometry software, and use various representations to help understand the effects of simple transformations and their compositions.

G.GCO.3

Mostly covered
Describe rotations and reflections that carry a regular polygon onto itself and identify types of symmetry of polygons, including line, point, rotational, and self-congruence, and use symmetry to analyze mathematical situations.

G.GCO.4

Mostly covered
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.GCO.5

Mostly covered
Predict and describe the results of transformations on a given figure using geometric terminology from the definitions of the transformations, and describe a sequence of transformations that maps a figure onto its image.

G.GCO.6

Partially covered
Demonstrate that triangles and quadrilaterals are congruent by identifying a combination of translations, rotations, and reflections in various representations that move one figure onto the other.

G.GCO.7

Partially covered
Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions.

G.GCO.8

Prove, and apply in mathematical and real-world contexts, theorems about lines and angles, including the following:

G.GCO.8a

Fully covered
Vertical angles are congruent.

G.GCO.8b

Fully covered
When a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles are supplementary.
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G.GCO.8c

Not covered
Any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment.
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G.GCO.8d

Not covered
Perpendicular lines form four right angles.
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G.GCO.9

Prove, and apply in mathematical and real-world contexts, theorems about the relationships within and among triangles, including the following:

G.GCO.9a

Fully covered
Measures of interior angles of a triangle sum to 180°.

G.GCO.9b

Not covered
Base angles of isosceles triangles are congruent.
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G.GCO.9c

Not covered
The segment joining midpoints of two sides of a triangle is parallel to the third side and half the length.
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G.GCO.9d

Not covered
The medians of a triangle meet at a point.
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G.GCO.10

Prove, and apply in mathematical and real-world contexts, theorems about parallelograms, including the following:

G.GCO.10a

Mostly covered
Opposite sides of a parallelogram are congruent.
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G.GCO.10b

Mostly covered
Opposite angles of a parallelogram are congruent.
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G.GCO.10c

Mostly covered
Diagonals of a parallelogram bisect each other.
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G.GCO.10d

Fully covered
Rectangles are parallelograms with congruent diagonals.
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G.GCO.10e

Mostly covered
A parallelograms is a rhombus if and only if the diagonals are perpendicular.
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G.GCO.11

Mostly covered
Construct geometric figures using a variety of tools, including a compass, a straightedge, dynamic geometry software, and paper folding, and use these constructions to make conjectures about geometric relationships.