Geometry CC 2015-2016
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 addit ion; 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. CPCFC – proofs with CPCFC
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)
2. 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)
3. Introduce Similarity and Dilations o Similarity theorems (AA ASA SAS)-proofs o Show how to find the center of dilation o Proofs with dilation
4. Triangle proportionality and mid-segment theorem
5. Dilation Proofs
6. Geometric Mean
7. Apps
8. Test

Unit 7: Right triangle Trig
1. Essential skills: o vocabulary of a right triangle (OHA) and Pythagorean theorem
2. Basic trig ratios: set up trig ratios o Real life apps
3. Solving trig ratios, real life apps o (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
2. Algebraic applications using properties
Thm sheets (If and only if) necessary and sufficient
3. Coordinate Geometry proofs: review triangles, trapezoids and kites
4. Coordinate Geometry proofs: review trapezoids, parallelograms
5. Euclidean Proofs (mini proofs based on diagrams with markings) o 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.
6. Euclidean and Transformation proofs
7. Applications
8. 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
2. Angles of a circle do now: tangents and secants
HW: flashcards
3. 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
4. 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
5. Circle Proofs
Do Now: intersecting chord similar triangles proof and 2 secants proof
Practice: big circle problem
6. Apps
7. Test
Geometry CC Regents
YEAR AT A GLANCE
Unit 1: Geometric transformations (8 blocks)
Unit 2: Angles and lines (8 blocks) (test Monday/Tuesday before Thanksgiving)
Unit 3: Triangles (6 blocks)
Unit 4: Triangle congruence (8 blocks)
Unit 5: Similarity transformations (8 blocks)
Unit 6: Right triangle relationships and trigonometry (5 blocks)
Unit 7: Quadrilaterals (8 blocks)
Unit 8: Geometric modeling in two dimensions &
Understanding and modeling with three-dimensional figures (6 blocks)
Unit 9: Circles (4.5 blocks) CURRENT 11 or 12 including old & new