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 (engageny.org). 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

Apps

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

Applications

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

Apps