Geometry I

This course covers Common Core Geometry standards and serves as an introduction to Common Core Geometry for students who need it. The following topics will be covered: congruence, similarity, right triangles, trigonometry, circles, geometric properties with equations, measurement and dimensions and modeling (engageny.org)

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%
  • 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.
  • 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, 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, 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: Explore compositions and identifying sequences of rigid motion.

Applications

Finding Angles: Learn about 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.

Apps

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

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

Inequalities: Explore 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.

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

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

Introduce Similarity and Dilations

  • Show how to find the center of dilation.
  • Proofs with dilation.

Triangle proportionality and mid-segment theorem

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: Practice trig and Pythagorean theorem modeling problems.

Find lines of symmetry for each quadrilateral

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: Explore pyramids.

Volume: Learn about non polyhedrons (spheres, cylinders, cones); reference sheet, applications; derive formulas.

Cross-section of prisms, pyramids, cylinders, cones, spheres (include Cavalieri’s principle)

Application problems

Essential Skills: Solve 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 a circle: Learn about chords equidistant and parallel chords, tangents, secants and chord lengths.

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