G.2D.1

Discover, evaluate, and analyze the relationships between lines, angles, and polygons to solve real-world and mathematical problems; express proofs in a form that clearly justifies the reasoning (e.g., two-column proofs, paragraph proofs, flowcharts).

G.2D.1.1Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems.G.2D.1.10Construct logical arguments to prove triangle similarity (AA, SSS, SAS).G.2D.1.11Use numeric, graphic, and algebraic representations of transformations in two dimensions (e.g., reflections, translations, dilations, rotations about the origin by multiples of 90') to solve problems involving figures on a coordinate plane and identify types of symmetry.G.2D.1.2Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs.G.2D.1.3Apply the properties of angles (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs.G.2D.1.4Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs.G.2D.1.5Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs.G.2D.1.6Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.G.2D.1.7Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).G.2D.1.8Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning.G.2D.1.9Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL).
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