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COMMON CORE REGENTS Exams
COMMON CORE GEOMETRY
Topic A: Definitions and Constructions
Concept 1: Angle Bisectors, Perpendicular Bisectors
Concept 2: Midpoints and the Midpoint Formula
Concept 3: Distance between two Points; The Distance Formula
Concept 4: Six Basic Constructions Using a Compass and Straight Edge
Topic B: Angles, Triangles & Parallel Lines
Concept 1: Vertical, Adjacent, Supplementary & Complementary Angles
Concept 2: Segments in Triangles: Altitude, Median, Angle Bisector
Concept 3: Sum of the Measures of the Angles of a Triangle
Concept 4: Isosceles and Equilateral Triangles
Concept 5: Problems involving Parallel Lines
Concept 6: Interior & Exterior Angles of a Triangle
Concept 7: CONSTRUCTION: Parallel Lines
Topic C: Postulates and Proofs
Concept 1: Connectives in logic; and, or, not, if...then, if and only if
Concept 2: Conditional Statements: Inverse, Converse, Contrapositive
Concept 3: Reflexive, Symmetric, Transitive, & Substitution Postulates
Concept 4: Addition, Subtraction, Multiplication. & Division Postulates
Concept 5: Using Postulates and Definitions in Proofs
Concept 6: Using Angle Theorems in Proofs
Topic D: Transformation Geometry
Concept 1: Line Reflections and Line Symmetry
Concept 2: Rotations
Concept 3: Point Reflections and Point Symmetry
Concept 4: Translations
Concept 5: Compositions of Transformations
Topic E: Congruence and Congruent Triangles
Concept 1: Congruent Triangles; Identifying the Method of Congruence
Concept 2: Proving Triangles Congruent: SSS, SAS, AAS, ASA
Concept 3: HY-Leg Method
Concept 4: Corresponding Parts of Congruent Triangles (CPCTC)
Concept 5: Overlapping Triangles
Concept 6: The Isosceles and Equilateral Triangles
Concept 7: Proofs with Parallel and Perpendicular Lines
Concept 8: Constructing a Triangle Congruent to a Given Triangle
Topic F: Properties of Quadrilaterals: Parallelograms, Trapezoids
Concept 1: The Parallelogram
Concept 2: The Rectangle, Square, and Rhombus
Concept 3: The Trapezoid
Concept 4: Proofs with Parallelograms
Concept 5: The Kite
Topic G: Midsegments; Concurrency in Triangles; Angles in Polygons
Concept 1: Midsegment of a Triangle; Segment Parallel to 3rd Side of a Triangle
Concept 2: Segments in Triangles: Medians, Altitudes, Angle Bisectors, Perpendicular Bisectors
Concept 3: Concurrency in the Triangle: Centroid, Orthocenter, Incenter, Circumcenter
Concept 4: CONSTRUCTIONS: Centroid, Orthocenter, Incenter, Circumcenter
Concept 5: Interior & Exterior Angles of a Polygon
Concept 6: CONSTRUCTIONS: Square, Hexagon, Equilateral Triangle
Topic H: Inequalities, Inequality Proofs, Indirect Proofs
Concept 1: Inequalities in the Triangle
Concept 2: Inequality Proofs
Concept 3: Indirect Proofs
Topic J: Similar Polygons; Dilations; Proofs with Similar Triangles
Concept 1: Ratio and Proportion
Concept 2: Proportions in Similar Triangles and Polygons
Concept 3: Dilations; Scale Factor; Compositions of Transformations
Concept 4: Dilations with Different Centers: CONSTRUCTION: Dilations & Finding Center of Dilation
Concept 5: Finding the Equation of a Dilated Line
Concept 6: Area Relationships in Similar Polygons
Concept 7: Dividing a Segment into a Given Ratio; CONSTRUCTION: Dividing a Segment into Equal Pieces
Concept 8: Proving Triangles Similar; Valid Methods of Determining if two Triangles are Similar
Concept 9: Proving Proportions and Products in Similar Triangles
Concept 10: Isometries and Orientation
Topic K: Proportions in the Right Triangle; Special Right Triangles; Trigonometry
Concept 1: Proportions in the Right Triangle; Altitude to the Hypotenuse
Concept 2: The Pythagorean Theorem
Concept 3: Special Right Triangles: 30-60-90 and 45-45-90
Concept 4: Basic Trigonometry: Soh Cah Toa
Concept 5: Problem-Solving with Trigonometry
Concept 6: Reciprocal Trigonometric Functions
Concept 7: Cofunctions
Concept 9: Law of Sines
Concept 10: Law of Cosines
Concept 11: Area of a Triangle
Topic L : Area and Volume; Radian Measure
Concept 1: Finding Areas of Triangles
Concept 2: Areas of Quadrilaterals
Concept 3: Area and Circumference of Circles
Concept 4: Radian Measure; Area of Sector; Length of an Arc
Concept 5: Finding Areas of Composite Figures; Finding Shaded Areas
Concept 6: Using the Apothem to find Areas of Polygons (Optional Topic)
Concept 7: Surface and Lateral Area
Concept 8: Volumes of Solids: Prisms, Cones, Cylinders, Spheres, Pyramids
Concept 9: Density, Volume and Cavalieri's Principle
Topic M: Coordinate Geometry; Slope and Equations of Lines; Systems of Equations
Concept 1: Slope of a line
Concept 2: Equation of a Line; y = mx + b
Concept 3: Determining if a Point is on a Line
Concept 4: Finding the Equation of a Line
Concept 5: The Midpoint of a Line Segment
Concept 6: Graphing a Line
Concept 8: Finding the Equation of a Perpendicular Bisector
Concept 9: Proofs in coordinate geometry
Concept 10: Proofs with Variable Coordinates
Concept 7: Parallel and Perpendicular Lines
Concept 11: Areas in coordinate geometry
Concept 12: Systems of Equations
Topic N: Geometry of the Circle
Concept 1: Equation of a Circle
Concept 2: Measures of Arcs and Angles: Central Angles
Concept 3: Measure of Inscribed Angles; Polygons Inscribed in the Circle
Concept 4: Measures of Angles formed by Tangents, Chords and Secants
Concept 5: Measures of Chords,Tangents and Secants
Concept 6: Circle Proofs
Topic O: Three-Dimensional Geometry (Optional Topic)
Concept 1: Three Dimensional Geometry: Points, Lines, Planes
Topic P: Locus (Optional Topic)
Concept 1: Locus theorems
Concept 2: Intersection of loci; loci in coordinate geometry
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