# Geometry Standards

 » MA.912.G.1.1 : Find the lengths and midpoints of line segments in two-dimensional coordinate systems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Points, Lines, Angles, and Planes » MA.912.G.1.2 : Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Points, Lines, Angles, and Planes » MA.912.G.1.3 : Identify and use the relationships between special pairs of angles formed by parallel lines and transversals. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Points, Lines, Angles, and Planes

MA.912.G.2 Polygons
 » MA.912.G.2.1 : Identify and describe convex, concave, regular, and irregular polygons. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Polygons » MA.912.G.2.2 : Determine the measures of interior and exterior angles of polygons, justifying the method used. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polygons » MA.912.G.2.3 : Use properties of congruent and similar polygons to solve mathematical or real-world problems. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Polygons » MA.912.G.2.4 : Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Polygons » MA.912.G.2.5 : Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polygons » MA.912.G.2.7 : Determine how changes in dimensions affect the perimeter and area of common geometric figures. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polygons

MA.912.G.4 Triangles
 » MA.912.G.4.1 : Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Triangles » MA.912.G.4.2 : Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors,orthocenter, centroid, incenter, and circumcenter. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Triangles » MA.912.G.4.3 : Construct triangles congruent to given triangles. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Triangles » MA.912.G.4.4 : Use properties of congruent and similar triangles to solve problems involving lengths and areas. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Triangles » MA.912.G.4.5 : Apply theorems involving segments divided proportionally. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Triangles » MA.912.G.4.6 : Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Triangles » MA.912.G.4.7 : Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Triangles

MA.912.G.5 Right Triangles
 » MA.912.G.5.1 : Prove and apply the Pythagorean Theorem and its converse. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Right Triangles » MA.912.G.5.2 : State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Right Triangles » MA.912.G.5.3 : Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Right Triangles » MA.912.G.5.4 : Solve real-world problems involving right triangles. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Right Triangles

MA.912.G.7 Polyhedra and Other Solids
 » MA.912.G.7.1 : Describe and make regular, non-regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice versa. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polyhedra and Other Solids » MA.912.G.7.2 : Describe the relationships between the faces, edges, and vertices of polyhedra. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polyhedra and Other Solids » MA.912.G.7.4 : Identify chords, tangents, radii, and great circles of spheres Cognitive Complexity: Level 1: Recall | Date Adopted or Revised: 09/07 Belongs to: Polyhedra and Other Solids » MA.912.G.7.5 : Explain and use formulas for lateral area, surface area, and volume of solids. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polyhedra and Other Solids » MA.912.G.7.6 : Identify and use properties of congruent and similar solids. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polyhedra and Other Solids » MA.912.G.7.7 : Determine how changes in dimensions affect the surface area and volume of common geometric solids. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Polyhedra and Other Solids

MA.912.G.8 Mathematical Reasoning and Problem Solving
 » MA.912.G.8.1 : Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Mathematical Reasoning and Problem Solving » MA.912.G.8.2 : Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Mathematical Reasoning and Problem Solving » MA.912.G.8.3 : Determine whether a solution is reasonable in the context of the original situation. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Mathematical Reasoning and Problem Solving » MA.912.G.8.4 : Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Mathematical Reasoning and Problem Solving » MA.912.G.8.5 : Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Mathematical Reasoning and Problem Solving » MA.912.G.8.6 : Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing, and drawing geometric figures. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 09/07 Belongs to: Mathematical Reasoning and Problem Solving

MA.912.T.2 Trigonometry in Triangles
 » MA.912.T.2.1 : Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Trigonometry in Triangles

MA.912.D.6 Logic
 » MA.912.D.6.2 : Find the converse, inverse, and contrapositive of a statement Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Logic » MA.912.D.6.3 : Determine whether two propositions are logically equivalent. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Logic » MA.912.D.6.4 : Use methods of direct and indirect proof and determine whether a short proof is logically valid. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 09/07 Belongs to: Logic

MA.912.G.6 Circles

LACC.1112.RST.2 Craft and Structure
 » LACC.1112.RST.2.4 : Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 12/10 Belongs to: Craft and Structure

LACC.910.RST.2 Craft and Structure
 » LACC.910.RST.2.4 : Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 12/10 Belongs to: Craft and Structure

LACC.1112.RST.3 Integration of Knowledge and Ideas
 » LACC.1112.RST.3.7 : Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning | Date Adopted or Revised: 12/10 Belongs to: Integration of Knowledge and Ideas

LACC.910.RST.3 Integration of Knowledge and Ideas
 » LACC.910.RST.3.7 : Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts | Date Adopted or Revised: 12/10 Belongs to: Integration of Knowledge and Ideas