• Geometry 2023-2024

     

    Unit 0 Pre Requisite Skills

    1. Solving Equations – include equations with fractions

    2. Parallel and Perpendicular Lines – slope formula, getting into y=, writing equations of parallel and perpendicular lines

    3. Writing Equations – given slope and y-intercept, given 2 points, etc

    4. Radicals and the Pythagorean Theorem – simplify radicals, add/sub/mult radicals

     

    Unit 1 Basic Constructions

    1. Essential Skills – naming segments, points, rays, planes, angles, etc; classifying angles – acute, obtuse, right, straight; definitions of bisect, midpoint, etc.; classify triangles by angles and sides

    2. Equilateral Triangles  construct equilateral and isosceles triangles, inscribed square and hexagon; copy segments

    3. Bisectors – copy and bisect an angle; construct perpendicular bisector

    4. Concurrences – construct circumcenter, incenter;and inscribe and circumscribe a circle about a triangle; concurrences theorems

    5. Concurrences - construct centroid, orthocenter concurrences theorems

    6. Parallel Lines and Apps – construct parallel lines

    7. Unit Test

     

    Unit 2 Rigid Motion

    1. Essential Skills – identify reflections, translations, rotations, dilations, line of symmetry, point symmetry, rotational symmetry, angles of rotation, degree and order of rotation

    2. Rigid Motion Exploration – ABCD preservation method for rigid motion; orientation

    3. Coordinate Plane – transformation rules in the coordinate plane

    4. Sequences – compositions and identifying sequences of rigid motion

    5. Compositions – more compositions and sequences

    6. Applications

    7. Test

     

    Unit 3 Unknown Angles

    1. Essential Skills writing good definitions; identifying complementary, supplementary, vertical, adjacent angles, alternate interior, alternate exterior, corresponding, interior on the same side angles; segment and angle addition; geometry’s undefined terms; reflexive, symmetric, and transitive postulates; auxiliary  lines

    2. Finding Angles – 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

    3. Transversal Angles parallel lines angles and auxiliary lines

    4. Intro to Proofs – paragraph proofs, two column proofs, flowchart proofs

    5. Coordinate Proofs – proofs using midpoint and slope; parallel lines and perpendicular lines and relationships to slope

    6. Apps

    7. Test









    Unit 4 Triangles

    1. Triangle Angles – sum of interior angles of a triangle theorem, exterior angle of a triangle theorem

    2. Isosceles Triangle Theorems – parts of an isosceles triangle; isosceles triangle theorems

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

    4. Concurrence on Coordinate Plane – determine the equation of a perpendicular line; centroid formula; find the circumcenter algebraically 

    5. Concurrence off Coordinate Plane – revisit constructing concurrences; divide a segment into congruent pieces

    6. Quest



    Unit 5 Triangle Congruence

    1. Triangles Congruence Statements – identifying corresponding parts

    2. Congruence Theorems – AAS, ASA, SSS, SAS, no AAA, ASS

    3. Congruence Theorems Part 2 – more proofs with triangle congruence

    4. CPCTC – proofs with CPCTC

    5. HL – hypotenuse leg theorems

    6. Isosceles Triangle Proofs – proofs using isosceles triangle theorems

    7. Overlapping Triangles

    8. Apps

    9. Unit Test

     

    Midterm

     

    Unit 6 Similarity and Dilations

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

         (HW: Prove Isosceles Right Triangle)

    1. Real life Apps: 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 - board is cut...) 2-1 (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)

    2. Introduce Similarity and Dilations

      • Similarity theorems (AA ASA SAS)-proofs

      • Show how to find the center of dilation

      • Proofs with dilation

    3. Triangle proportionality and mid-segment theorem

    4. Dilation Proofs

    5. Geometric Mean 

    6. Apps

    7. Test








    Unit 7: Right triangle Trig

    1. Essential skills:

      • vocabulary of a right triangle (OHA) and Pythagorean theorem 

    2. Basic trig ratios: set up trig ratios

      • Real life apps

    3. Solving trig ratios, real life apps

      • (Explain and use the relationship between the sine and cosine of complementary angles.)

    4. Apps - trig and Pythagorean thm modeling problems

    5. Quest

     

    Unit 8: Quads

    1. Essential skills: Quadrilateral Lab

    Find lines of symmetry for each quadrilateral

    Matrix for HW

    1. Algebraic applications using properties

    Thm sheets (If and only if) necessary and sufficient

    1. Coordinate Geometry proofs: review triangles, trapezoids and kites

    2. Coordinate Geometry proofs: review trapezoids, parallelograms

    3. 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.

    NYSED: Theorems include but are not limited to the listed theorems. Example: rhombus is a parallelogram with perpendicular diagonals. 

    1. Euclidean and Transformation proofs

    2. Applications

    3. Test

     

    Unit 9: Geometric measurement

    1. Essential Skills 2-Dimensional- multi-step problems; Hand out Formula Sheet; Unit Conversions  (Hand out NYS reference sheet)

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

    3. Volume: pyramids 

    4. Volume: non polyhedrons - spheres, cylinders, cones (reference sheet, applications), derive formulas

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

    6. Application problems 

    7. Test HW: circle vocab ppt 

     













     Unit 10: Circles

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

    Quiz: circle vocab (ppt)

    Do Now: construct figures in a circle: equilateral triangle, hexagon and square

    1. Angles of a circle
      do now: tangents and secants

    HW: flashcards

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

    Do now: quadrilaterals inscribed in a circle and similarity of concentric and other circles

    HW: flashcards

    1. Arc length and area of sector, derive the formula for the area of sectors, radian measure, S=OR

    Do Now: degrees and radians

                  Quiz on circle angles

    1. Circle Proofs

    Do Now: intersecting chord similar triangles proof and 2 secants proof

                   Practice:  big circle problem

    1. Apps

    2. Test

     

    Geometry Regents Exam in June
Last Modified on November 9, 2023