CC Geometry

This course covers Common Core geometry standards. The following topics will be covered: congruence, similarity, right triangles, trigonometry, circles, geometric properties with equations, measurement and dimensions and Modeling ( At the end of the course, students will be able to define geometric terms understand formal Euclidean constructions and effects of rigid motions; show congruence with rigid motions; explain and use the definition of similarity in transformations; understand similarity proofs and ratios in similar figures; prove theorems of lines, angles, triangles and parallelograms; determine circumference and area of circles; calculate volume of cylinders, pyramids and cones; use volumes in application problems; understand directed line segments, coordinate proofs angles and chords in circles; and perform equations of circles and lines.

Required Supplies

  • Binder
  • Loose-leaf paper
  • Compass
  • Graphing calculator suggested for homework (a classroom set is available in school)

Course Format and Procedures

The course structure includes lectures, inquiry-based learning (i.e., flipped classroom), project-based learning, collaborative activities and weekly quizzes (5-40 minutes in duration). Students are expected to take notes daily; complete homework when assigned; make up missed work in a timely manner; refrain from using electronic devices (such as cell phones, mp3 players, laptops, tablets, etc.), in class; direct questions at the instructor, not other students.

Grading Procedures

  • Quizzes (weekly): 100%
  • Homework: Insufficiently completed homework will be result in the deduction of points from a student’s average:
    • Homework grade of “0” (not done or minimal work applied): 1 point off average)
    • Homework grade of “–“ (partially done): ½ point off average
    • Homework grade of “✔” (completed): no points deducted
  • Midterm and final exams: 10%

Student and Parent Resources

  • Students who are struggling during the semester should seek immediate help from the instructor during math lab or after school.
    • Google Classroom: 6wrcz7
  • Parent Resources:  
    • Parent Portal
    • Google Classroom
    • Regents Prep Online Database
    • Khan Academy
    • Email the instructor or schedule a meeting through the guidance department

Course Outline

Essential Skills: Name segments, points, rays, planes, angles, etc.; classify angles (acute, obtuse, right, and straight); define bisect, midpoint, etc.; classify triangles by angles and sides.

Equilateral Triangles: Construct equilateral and isosceles triangles, inscribed square and hexagon; copy segments.

Bisectors: Copy and bisect an angle; construct perpendicular bisector.

Concurrences: Construct circumcenter, incenter; and inscribe and circumscribe a circle about a triangle; concurrences theorems.

Concurrences: Construct centroid, orthocenter concurrences theorems.

Parallel Lines and Apps: Construct parallel lines.

Essential Skills: Identify reflections, translations, rotations, dilations, line of symmetry, point symmetry, rotational symmetry, and angles of rotation, degree and order of rotation.

Rigid Motion Exploration: Learn ABCD preservation method for rigid motion, orientation.

Coordinate Plane: Explore transformation rules in the coordinate plane.

Sequences: Learn about compositions and identify sequences of rigid motion.

Essential Skills: Write good definitions; identify complementary, supplementary, vertical, adjacent, alternate interior, alternate exterior, corresponding and interior on the same side angles; perform segment and angle addition; learn geometry’s undefined terms; explore reflexive, symmetric and transitive postulates; learn about auxiliary lines.

Finding Angles: Learn small algebraic proofs with angles; sum of angles on a straight line is 180; the sum of adjacent angles around a point is 360; vertical angles are congruent.

Transversal Angles: Explore parallel lines angles and auxiliary lines.

Intro to Proofs: Learn about paragraph proofs, two column proofs, flowchart proofs.

Coordinate Proofs: Explore proofs using midpoint and slope; parallel lines and perpendicular lines; and relationships to slope.

Triangle Angles: Learn sum of interior angles of a triangle theorem; exterior angle of a triangle theorem.

Isosceles Triangle Theorems: Learn parts of an isosceles triangle; isosceles triangle theorems.

Inequalities – Learn triangle inequality theorem; largest angle across from the longest side; exterior angle inequality theorem.

Concurrence on Coordinate Plane: Determine the equation of a perpendicular line; centroid formula; find the circumcenter algebraically.

Concurrence off Coordinate Plane: Revisit constructing concurrences; divide a segment into congruent pieces.

Triangles Congruence Statements: Identifying corresponding parts.

Congruence Theorems: AAS, ASA, SSS, SAS, no AAA, ASS.

Congruence Theorems Part 2: Explore more proofs with triangle congruence
CPCTC: Learn proofs with CPCTC

HL: Learn hypotenuse leg theorems

Isosceles Triangle Proofs: Explore proofs using isosceles triangle theorems.

Essential skills: Derive distance formula and investigate (graphically); use distance formula to find area and perimeter of figures.

Real-life Apps: Learn ratios, proportions and scale factors (i.e., find the point on a directed line segment between two given points that partitions the segment in a given ratio, board is cut…); 2-1 (e.g., design an object or structure to satisfy physical constraints or minimize cost; work with typographic grid systems based on ratios.)

Introduce Similarity and Dilation

  • Similarity theorems: (AA ASA SAS) proofs
  • Show how to find the center of dilation
  • Proofs with dilation

Triangle proportionality and mid-segment theorem

Dilation Proofs

Geometric Mean


Essential skills: Learn vocabulary of a right triangle (OHA) and Pythagorean theorem.

Basic trig ratios: Set up trig ratios

  • Real-life apps
  • Solving trig ratios, real life apps
  • Explain and use the relationship between the sine and cosine of complementary angles

Apps: Learn trig and Pythagorean theorem modeling problems.

Essential skills: Quadrilateral lab.

Find lines of symmetry for each quadrilateral

Coordinate geometry proofs: Review triangles, trapezoids and kites.

Coordinate geometry proofs: Review trapezoids, parallelograms.

Euclidean proofs: Mini-proofs based on diagrams with markings.

Prove theorems about parallelograms. Theorems include: Opposite sides are congruent; opposite angles are congruent; the diagonals of a parallelogram bisect each other; and, conversely, rectangles are parallelograms with congruent diagonals.

Euclidean and transformation proofs


Essential Skills 2-Dimensional: Perform multi-step problems; hand out formula sheet; learn unit conversions; hand out NYS reference sheet.

Volume: Explore prisms (rectangular, triangular, etc.); use reference sheets, applications, work backwards and derive formulas.

Volume: Pyramids.

Volume: Learn non polyhedrons (e.g., spheres, cylinders, cones); reference sheet; applications; derive formulas.
Cross-section of prisms, pyramids, cylinders, cones, spheres (include Cavalieri’s principle).

Application problems

Essential Skills: Learn equation of circle; graph circle on coordinate plane; derive the equation of a circle in center-radius form by completing the square.

Angles of a circle

Segments in circle-chords equidistant and parallel chords, tangents, secants, chord lengths.

Arc length and area of sector: Derive the formula for the area of sectors, radian measure, S=OR

Circle Proofs