NYS Learning Standards Basic Geometry

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Select the number of each type of objective: (Selecting Random will randomly generate all subtypes) Click on any title to see the free sample worksheet. (only the first few samples are free) (Random) G-CO.A.1-5 Experiment with transformations in the plane. a. Defining Common Notation b. Using Point, Line, and Plane Postulates c. Using the Distance Formula d. Finding Points using Distance e. Identifying Line Symmetry f. Identifying Rotational and Point Symmetry g. Identifying the Transformation (Rotation, Reflection, Translation, or Glide Reflection) h. Reflecting Twice i. Applying Rotations j. Applying Reflections k. Applying Translations (with Vectors) l. Composition of Transformations m. Applying Glide Reflections n. Classifying Frieze Patterns o. Finding the Minimum Distance between two Points Touching a Line p. Finding Arc Length (Random) G-CO.B.6-8 Understand congruence in terms of rigid motions. a. Writing Congruence Statements for Triangles b. Using Triangle Congruence Theorems c. Filling in Reasons for Proving Triangles are Congruent d. Proving Triangles are Congruent e. Using Triangle Congruence to find a Missing Point f. Filling in Reasons when Using CPCTC in Proofs g. Using CPCTC in Proofs h. Proving Congruent with Coordinate Proofs (Random) G-CO.C.9-11 Prove geometric theorems. a. Identifying Complementary, Supplementary, and Congruent Angles b. Using Complementary, Supplementary, and Congruent Angles c. Using the Definition of Bisect d. Using the Vertical Angle Theorem e. Using the Linear Pair Postulate f. Using the Triangle Sum Theorem to Find Angle Measures g. Using the Exterior Angle Theorem to Find Angle Measures h. Finding Angle Measures (Combinations of the Above) i. Naming Angle Pairs when given Two Lines and a Transversal (does not include Same-Side Exterior) j. Identifying Angle Relationships when given Two Parallel Lines and a Transversal k. Deciding when Lines are Parallel Given Two Lines and a Transversal l. Finding the value of x to prove two Lines are Parallel m. Filling in Reasons for Proofs Involving Transversals n. Proofs Involving Transversals o. Identifying Angle Bisectors, Perpendicular Bisectors, Medians, Altitudes, and Midsegments p. Finding the Endpoints of the Triangle given the Endpoints of the Midsegments q. Using Midsegments in Triangles r. Identifying Properties of Parallelograms s. Proving Quadrilaterals are Parallelograms (Random) G-CO.D.12-13 Make geometric constructions. a. Identifying Constructions b. Using Constructions (Basic) c. Using Constructions (Complex) (Random) G-SRT.A.1-3 Understand similarity in terms of similarity transformations. a. Writing Similarity Statements and Statements of Proportion for Triangles b. Using Triangle Similarity to find a Missing Point c. Finding the Scale Factor d. Using Proportions in Similar Triangles e. Using Proportional Reasoning with Similar Objects f. Using Scale Factors in Dilations (Random) G-SRT.B.4-5 Prove theorems involving similarity. a. Simplifying Radicals b. Finding the Geometric Mean c. Using the Pythagorean Theorem Converse (Classifying Triangles) d. Using Right Triangles with Altitudes e. Using Triangle Similarity Theorems f. Filling in Reasons when Proving Triangles are Similar g. Proving Triangles are Similar	(Random) G-SRT.C.6-8 Define trigonometric ratios and solve problems involving right triangles. a. Using the Pythagorean Theorem b. Using Special Right Triangles c. Finding Trigonometric Functions from Triangles d. Solving Ratios with Trigonometric Functions e. Using Trigonometry (Sin, Cos, Tan) to find Side Lengths f. Using Inverse Trigonometric Functions (Sin^-1, Cos^-1, Tan^-1) to find Angles g. Solving Right Triangles (Random) G-SRT.D.9 Apply Trigonometry to general triangles. a. Finding Area of Right Triangles (Uses Trig!) b. Finding Area using Sine (Random) G-C.A.1-2 Understand and apply theorems about circles. a. Reviewing Circle Vocabulary b. Using Tangent Properties c. Finding Arcs/Angles (Central Angle) d. Finding Arcs/Angles (Inscribed Angles) e. Finding Miscellaneous Angles f. Using Diameters and Chords g. Identifying a Tangent to a Circle (using Pythagorean Theorem) h. Identify points as Inside, Outside, or On a Circle Given the Equation i. Combining Triangles/Quadrilaterals And Circles (Segments) j. Combining Triangles/Quadrilaterals And Circles (Angles) (Random) G-GPE.A.1 Translate between the geometric description and the equation of a conic section. a. Identifying and Creating Equations of Circles b. Creating Equations of Circles from 2 Key Points (Random) G-GPE.B.4-7 Use coordinates to prove simple geometric theorems algebraically. a. Writing Equations of Parallel Lines b. Writing Equations of Perpendicular Lines c. Identifying Parallel, Perpendicular, and Oblique from Equations d. Identifying Parallel, Perpendicular, and Skew e. Finding Area and Perimeter of Rectangles and Squares (Given Coordinates) f. Finding Area and Perimeter of Triangles (Given Coordinates) g. Finding Area and Circumference of Circles (Given Coordinates) h. Using the Midpoint Formula i. Using the Formula for Slope j. Finding Angles, Sides, and Diagonals in Parallelograms k. More complicated problems with Parallelograms l. Placing figures Conveniently in the Coordinate Plane m. Using The Apothem to find Area of a Polygon n. Using The Radius to find Area of a Polygon o. Using The Side Length to find Area of a Polygon p. Finding Points using Slope q. Proving Quadrilaterals are Special Parallelograms using Coordinate proofs (Random) G-GMD.A.1 and 3 Explain volume formulas and use them to solve problems. a. Finding the Surface Area b. Finding the Volume Problems c. Solving for x Given Volume d. Finding Volume of Pyramids and Cones (with distractors) (Random) G-GMD.B.4 Visualize relationships between two-dimensional and three-dimensional objects. a. Creating a 2-D Representation of a 3-D Object b. Creating a 3-D Object from 2-D Representations c. Creating a 3-D Object from Nets (Random) G-MG.A.1-3 Apply geometric concepts in modeling situations. a. Word Problems with Similar Triangles b. Area Word Problems c. Word Problems d. Solving Word Problems e. Word Problems (requires Trigonometry) f. Surface Area and Volume Word Problems g. Using Scale Drawings h. Using Perspective Drawings i. Using Blueprints
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