OCG - Geometry

South Carolina Standards: 

 South Carolina College- and Career-Ready (SCCCR) Geometry
● Standards denoted by an asterisk (*) are SCCCR Graduation Standards.
● The SC standards highlighted in yellow are appropriate for honors level geometry and are
supplemental topics to SCCC Geometry.
● The SC standards highlighted in green are appropriate for probability and statistics.
Circles
The student will:
G.GCI.1 Prove that all circles are similar.
G.GCI.2*
Identify and describe relationships among inscribed angles, radii, and chords;
among inscribed angles, central angles, and circumscribed angles; and between
radii and tangents to circles. Use those relationships to solve mathematical and
real-world problems.
G.GCI.3 Construct the inscribed and circumscribed circles of a triangle using a variety of
tools, including a compass, a straightedge, and dynamic geometry software, and
prove properties of angles for a quadrilateral inscribed in a circle.
G.GCI.4 Construct a tangent line to a circle through a point on the circle, and construct a
tangent line from a point outside a given circle to the circle; justify the process
used for each construction.
G.GCI.5* Derive the formulas for the length of an arc and the area of a sector in a circle
and apply these formulas to solve mathematical and real-world problems.
Congruence
The student will:
G.GCO.1* 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* 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* 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* Develop definitions of rotations, reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.
G.GCO.5* 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* 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* 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:
a. vertical angles are congruent;
b. when a transversal crosses parallel lines, alternate interior angles are
congruent, alternate exterior angles are congruent, and consecutive interior
angles are supplementary;
c. any point on a perpendicular bisector of a line segment is equidistant from
the endpoints of the segment;
d. perpendicular lines form four right angles.
G.GCO.9* Prove, and apply in mathematical and real-world contexts, theorems about the
relationships within and among triangles, including the following:
a. measures of interior angles of a triangle sum to 180°;
b. base angles of isosceles triangles are congruent;
c. the segment joining midpoints of two sides of a triangle is parallel to the third
side and half the length;
d. the medians of a triangle meet at a point.
G.GCO.10* Prove, and apply in mathematical and real-world contexts, theorems about
parallelograms, including the following:
a. opposite sides of a parallelogram are congruent;
b. opposite angles of a parallelogram are congruent;
c. diagonals of a parallelogram bisect each other;
d. rectangles are parallelograms with congruent diagonals;
e. a parallelograms is a rhombus if and only if the diagonals are
perpendicular.
G.GCO.11* 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.
Geometric Measurement and Dimension
The student will:
G.GGMD.1* Explain the derivations of the formulas for the circumference of a circle, area of a circle,
and volume of a cylinder, pyramid, and cone. Apply these formulas to solve
mathematical and real-world problems.
G.GGMD.2 Explain the derivation of the formulas for the volume of a sphere and other solid figures
using Cavalieri’s principle.
G.GGMD.3* Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, and
spheres to solve problems and justify results. Include problems that involve algebraic
expressions, composite figures, geometric probability , and real-world applications.
G.GGMD.4 * Describe the shapes of two-dimensional cross-sections of three-dimensional objects
and use those cross-sections to solve mathematical and real-world problems.
Expressing Geometric Properties with Equations
The student will:
G.GGPE.1* Understand that the standard equation of a circle is derived from the definition of a circle
and the distance formula.
G.GGPE.4* Use coordinates to prove simple geometric theorems algebraically.
G.GGPE.5* Analyze slopes of lines to determine whether lines are parallel, perpendicular, or
neither. Write the equation of a line passing through a given point that is parallel or
perpendicular to a given line. Solve geometric and real-world problems involving lines
and slope.
G.GGPE.6 Given two points, find the point on the line segment between the two points that divides
the segment into a given ratio.
G.GGPE.7* Use the distance and midpoint formulas to determine distance and midpoint in a
coordinate plane, as well as areas of triangles and rectangles, when given coordinates.
Modeling
The student will:
G.GM.1* Use geometric shapes, their measures, and their properties to describe real-world
objects.
G.GM.2 Use geometry concepts and methods to model real-world situations and solve
problems using a model.
Similarity, Right Triangles, and Trigonometry
The student will:
G.GSRT.1 Understand 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. Verify
experimentally the properties of dilations given by a center and a scale factor.
Understand the dilation of a line segment is longer or shorter in the ratio given by the
scale factor.
G.GSRT.2* Use the definition of similarity to decide if figures are similar and justify decision.
Demonstrate that two figures are similar by identifying a combination of translations,
rotations, reflections, and dilations in various representations that move one figure onto
the other.
G.GSRT.3* Prove that two triangles are similar using the Angle-Angle criterion and apply the
proportionality of corresponding sides to solve problems and justify results.
G.GSRT.4* Prove, and apply in mathematical and real-world contexts, theorems involving
similarity about triangles, including the following:
a. A line drawn parallel to one side of a triangle divides the other two sides into
parts of equal proportion.
b. If a line divides two sides of a triangle proportionally, then it is parallel to the third
side.
c. The square of the hypotenuse of a right triangle is equal to the sum of
squares of the other two sides.
G.GSRT.5* Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
G.GSRT.6* Understand how the properties of similar right triangles allow the trigonometric ratios to
be defined and determine the sine, cosine, and tangent of an acute angle in a right
triangle.
G.GSRT.7 Explain and use the relationship between the sine and cosine of complementary
angles.
G.GSRT.8* Solve right triangles in applied problems using trigonometric ratios and the Pythagorean
Theorem.
Interpreting Data
The student will:
G.SPID.1* Select and create an appropriate display, including dot plots, histograms, and box plots,
for data that includes only real numbers.
G.SPID.2* Use statistics appropriate to the shape of the data distribution to compare center and
spread of two or more different data sets that include all real numbers.
G.SPID.3* Summarize and represent data from a single data set. Interpret differences in shape,
center, and spread in the context of the data set, accounting for possible effects of
extreme data points (outliers).

Other Standards:  (List national or local standards students are expected to master in this course)

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