Geometry (Virginia SOL)

Reasoning, Lines, and Transformations (RLT)

• G.RLT.1 Translate logic statements, identify conditional statements, and use and interpret Venn diagrams.
• Write propositional and compound statements symbolically, including geometric relationships.
• Identify the converse, inverse, and contrapositive and judge their truth; relate biconditionals to true conditionals.
• Use Venn diagrams to show union, intersection, subset, and negation.
• Interpret Venn diagrams, including in context.
• G.RLT.2 Prove and justify angle relationships formed when parallel lines are cut by a transversal.
• Prove relationships of corresponding, alternate interior/exterior, and same-side interior/exterior angles.
• Prove lines are parallel from numerical or algebraic angle measures.
• Solve problems using angle relationships formed by parallel lines and transversals.
• G.RLT.3 Solve problems involving symmetry and transformations, including in context.
• Locate, count, and draw lines of symmetry of figures.
• Decide whether a figure has point symmetry, line symmetry, both, or neither.
• Identify the transformation or combination of transformations that maps a preimage to an image.

Triangles (TR)

• G.TR.1 Determine relationships between the angle measures and side lengths of triangles, including in context.
• Decide whether three given segment lengths can form a triangle.
• Find the range of possible lengths for a third side given two sides.
• Order the sides of a triangle by length from given angle measures.
• Order the angles of a triangle by measure from given side lengths.
• Find interior and exterior angles of a triangle given two angle measures.
• G.TR.2 Prove triangles congruent with direct and indirect proofs and solve problems using congruent triangles.
• Prove congruence using SSS, SAS, ASA, AAS, and HL.
• Prove triangle congruence using algebraic methods.
• Prove triangle congruence using coordinate methods (slope and distance formulas).
• Construct congruent triangles using segment, angle, and perpendicular constructions.
• G.TR.3 Prove triangles similar with direct and indirect proofs and solve problems using similar triangles, including in context.
• Prove similarity using SAS, SSS, and AA.
• Prove triangle similarity using algebraic methods.
• Prove triangle similarity using coordinate methods (slope and distance formulas).
• Describe sequences of transformations that show two coplanar triangles are similar.
• Solve problems involving attributes of similar triangles.
• G.TR.4 Model and solve problems with right-triangle trigonometry and the Pythagorean Theorem.
• Decide whether three given lengths form a right triangle.
• Find and verify trigonometric ratios using right triangles.
• Model and solve problems using sine, cosine, and tangent ratios.
• Solve problems using the properties of special right triangles.
• Find missing lengths in 45°-45°-90° triangles, rationalising denominators where needed.
• Find missing lengths in 30°-60°-90° triangles, rationalising denominators where needed.
• Solve problems using the Pythagorean Theorem, its converse, and Pythagorean triples.

Polygons and Circles (PC)

• G.PC.1 Prove and justify properties of quadrilaterals and use them to solve problems about sides, angles, and diagonals.
• Solve problems using properties of parallelograms, rectangles, rhombi, squares, and trapezoids.
• Prove quadrilateral properties using coordinate and algebraic methods.
• Prove quadrilateral theorems and properties using deductive reasoning.
• Use constructions to verify properties of quadrilaterals.
• G.PC.2 Verify relationships and solve problems about the sides and angles of convex polygons.
• Find the number of sides of a regular polygon from its angle measures.
• Justify interior and exterior angle-sum relationships and solve angle-sum problems.
• Justify the angle measures of regular polygons and solve related problems.
• G.PC.3 Solve problems, including in context, using properties of circles.
• Find proportional relationships between arc length or sector area and other parts of a circle.
• Find arc measures and angles involving central angles.
• Find arc measures and angles involving inscribed angles.
• Calculate arc length.
• Calculate the area of a sector.
• Use arc length or sector area to find unknown measures of a circle.
• G.PC.4 Solve problems in the coordinate plane involving equations of circles.
• Derive the equation of a circle from its center and radius using the Pythagorean Theorem.
• Find the center, radius, or diameter from a graph, equation, or endpoints; find points on a circle.
• Write the equation of a circle from a graph, center and point, center and radius, or diameter endpoints.

Two- and Three-Dimensional Figures (DF)

• G.DF.1 Create models and solve surface area and volume problems for prisms, cylinders, cones, pyramids, and spheres.
• Identify the shape of a two-dimensional cross section of a solid.
• Model and solve surface area problems, including composite figures.
• Solve multistep volume problems, including composite figures.
• Find unknown measurements from a side length, face area, or volume.
• G.DF.2 Determine how changing dimensions affects a figure and relate the original and changed figures.
• Describe how changes in dimensions affect perimeter, area, surface area, and volume.
• Describe how changes in surface area or volume affect one or more dimensions.
• Solve problems involving changed dimensions or derived measures.
• Compare ratios of side lengths, perimeters, areas, and volumes of similar figures.
• Recognize similar two- and three-dimensional figures and solve related problems.