Virginia Geometry Math Standards

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RLT Reasoning, Lines, and Transformations

• RLT.G.1 The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include
  • RLT.G.1.a identifying the converse, inverse, and contrapositive of a conditional statement;
  • RLT.G.1.b translating a short verbal argument into symbolic form
  • RLT.G.1.c determining the validity of a logical argument.
• RLT.G.2 The student will use the relationships between angles formed by two lines intersected by a transversal to
  • RLT.G.2.a prove two or more lines are parallel
  • RLT.G.2.b solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal.
  • Checkpoint opportunity
• RLT.G.3 The student will solve problems involving symmetry and transformation. This will include
  • RLT.G.3.a investigating and using formulas for determining distance, midpoint, and slope;
  • RLT.G.3.b applying slope to verify and determine whether lines are parallel or perpendicular
  • RLT.G.3.c investigating symmetry and determining whether a figure is symmetric with respect to a line or a point
  • RLT.G.3.d determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.
  • Checkpoint opportunity
• RLT.G.4 The student will construct and justify the constructions of
  • RLT.G.4.a a line segment congruent to a given line segment
  • RLT.G.4.b the perpendicular bisector of a line segment
  • RLT.G.4.c a perpendicular to a given line from a point not on the line
  • RLT.G.4.d a perpendicular to a given line at a given point on the line
  • RLT.G.4.e the bisector of a given angle,
  • RLT.G.4.f an angle congruent to a given angle
  • RLT.G.4.g a line parallel to a given line through a point not on the line
  • RLT.G.4.h an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
  • Checkpoint opportunity

T Triangles

• T.G.5 The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include
  • T.G.5.a ordering the sides by length, given angle measures;
  • T.G.5.b ordering the angles by degree measure, given side lengths;
  • T.G.5.c determining whether a triangle exists
  • T.G.5.d determining the range in which the length of the third side must lie.
• T.G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent.
• T.G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar.
  • Checkpoint opportunity
• T.G.8 The student will solve problems, including practical problems, involving right triangles. This will include applying
  • T.G.8.a the Pythagorean Theorem and its converse
  • T.G.8.b properties of special right triangles
  • T.G.8.c trigonometric ratios.
  • Checkpoint opportunity

PC Polygons and Circles

• PC.G.9 The student will verify and use properties of quadrilaterals to solve problems, including practical problems.
• PC.G.10 The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the
  • PC.G.10.a sum of the interior and/or exterior angles
  • PC.G.10.b measure of an interior and/or exterior angle
  • PC.G.10.c number of sides of a regular polygon.
• PC.G.11 The student will solve problems, including practical problems, by applying properties of circles. This will include determining
  • PC.G.11.a angle measures formed by intersecting chords, secants, and/or tangents;
  • PC.G.11.b lengths of segments formed by intersecting chords, secants, and/or tangents;
  • PC.G.11.c arc length
  • PC.G.11.d area of a sector.
  • Checkpoint opportunity
• PC.G.12 The student will solve problems involving equations of circles.
  • Checkpoint opportunity

TDF Three-Dimensional Figures

• TDF.G.13 The student will use surface area and volume of three-dimensional objects to solve practical problems.
  • Checkpoint opportunity
• TDF.G.14 The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include
  • TDF.G.14.a comparing ratios between lengths, perimeters, areas, and volumes of similar figures;
  • TDF.G.14.b determining how changes in one or more dimensions of a figure affect area and/or volume of the figure
  • TDF.G.14.c determining how changes in area and/or volume of a figure affect one or more dimensions of the figure
  • TDF.G.14.d solving problems, including practical problems, about similar geometric figures.